diff --git a/sql/core/src/main/scala/org/apache/spark/sql/execution/datasources/parquet/ParquetRowConverter.scala b/sql/core/src/main/scala/org/apache/spark/sql/execution/datasources/parquet/ParquetRowConverter.scala
index 9ffc2b5dd8a56..899c654e04a67 100644
--- a/sql/core/src/main/scala/org/apache/spark/sql/execution/datasources/parquet/ParquetRowConverter.scala
+++ b/sql/core/src/main/scala/org/apache/spark/sql/execution/datasources/parquet/ParquetRowConverter.scala
@@ -214,6 +214,10 @@ private[parquet] class ParquetRowConverter(
       updater: ParentContainerUpdater): Converter with HasParentContainerUpdater = {
 
     catalystType match {
+      case ByteType | ShortType | IntegerType | LongType | FloatType | DoubleType
+        if ParquetSchemaCompatibility.isCompatible(catalystType, parquetType) =>
+          ParquetSchemaCompatibility.newCompatibleConverter(parquetType, catalystType, updater)
+
       case BooleanType | IntegerType | LongType | FloatType | DoubleType | BinaryType =>
         new ParquetPrimitiveConverter(updater)
 
diff --git a/sql/core/src/main/scala/org/apache/spark/sql/execution/datasources/parquet/ParquetSchemaCompatibility.scala b/sql/core/src/main/scala/org/apache/spark/sql/execution/datasources/parquet/ParquetSchemaCompatibility.scala
new file mode 100644
index 0000000000000..3f15c68bbd3b9
--- /dev/null
+++ b/sql/core/src/main/scala/org/apache/spark/sql/execution/datasources/parquet/ParquetSchemaCompatibility.scala
@@ -0,0 +1,112 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *    http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package org.apache.spark.sql.execution.datasources.parquet
+
+import org.apache.parquet.io.api.Converter
+import org.apache.parquet.schema.Type
+
+import org.apache.spark.sql.catalyst.analysis.TypeCoercion
+import org.apache.spark.sql.types._
+
+private[parquet] object ParquetSchemaCompatibility {
+
+  private val schemaConverter = new ParquetSchemaConverter(writeLegacyParquetFormat = false)
+
+  // The logic for setting and adding a value in `ParquetPrimitiveConverter` are separated
+  // into `NumericValueUpdater` and `NumericCompatibleConverter` so that value can be converted
+  // to a desired type.
+  // `NumericValueUpdater` updates the input `Number` via `ParentContainerUpdater`. This
+  // is for updating a value converted for the appropriate value type for `ParentContainerUpdater`
+  private type NumericValueUpdater = Number => Unit
+
+  // This is a wrapper for `NumericValueUpdater`. this returns a converter that adds the value
+  // from `NumericValueUpdater`.
+  private type NumericCompatibleConverter = NumericValueUpdater => ParquetPrimitiveConverter
+
+  private def createCompatiblePrimitiveConverter(
+      parquetType: Type,
+      catalystType: DataType,
+      updater: ParentContainerUpdater): NumericCompatibleConverter = {
+
+    val catalystTypeFromParquet = schemaConverter.convertField(parquetType)
+
+    catalystTypeFromParquet match {
+      case ByteType | ShortType | IntegerType | LongType | FloatType | DoubleType =>
+        (valueUpdater: NumericValueUpdater) =>
+          new ParquetPrimitiveConverter(updater) {
+            override def addInt(value: Int): Unit = valueUpdater(value)
+            override def addLong(value: Long): Unit = valueUpdater(value)
+            override def addFloat(value: Float): Unit = valueUpdater(value)
+            override def addDouble(value: Double): Unit = valueUpdater(value)
+          }
+
+      case _ =>
+        throw new RuntimeException(
+          s"Unable to create Parquet converter for data type $catalystType " +
+            s"whose Parquet type is $parquetType. They are not compatible.")
+    }
+  }
+
+  def isCompatible(catalystType: DataType, parquetType: Type): Boolean = {
+    // Find a compatible type between both numeric types.
+    val catalystTypeFromParquet = schemaConverter.convertField(parquetType)
+    val compatibleCatalystType =
+      TypeCoercion.findTightestCommonTypeOfTwo(catalystType, catalystTypeFromParquet).orNull
+    catalystType == compatibleCatalystType
+  }
+
+  def newCompatibleConverter(
+      parquetType: Type,
+      catalystType: DataType,
+      updater: ParentContainerUpdater): Converter with HasParentContainerUpdater = {
+
+    val newCompatiblePrimitiveConverter =
+      createCompatiblePrimitiveConverter(parquetType, catalystType, updater)
+
+    catalystType match {
+      case ByteType =>
+        val valueUpdater: NumericValueUpdater = (v: Number) => updater.setByte(v.byteValue())
+        newCompatiblePrimitiveConverter(valueUpdater)
+
+      case ShortType =>
+        val valueUpdater: NumericValueUpdater = (v: Number) => updater.setShort(v.shortValue())
+        newCompatiblePrimitiveConverter(valueUpdater)
+
+      case IntegerType =>
+        val valueUpdater: NumericValueUpdater = (v: Number) => updater.setInt(v.intValue())
+        newCompatiblePrimitiveConverter(valueUpdater)
+
+      case LongType =>
+        val valueUpdater: NumericValueUpdater = (v: Number) => updater.setLong(v.longValue())
+        newCompatiblePrimitiveConverter(valueUpdater)
+
+      case FloatType =>
+        val valueUpdater: NumericValueUpdater = (v: Number) => updater.setFloat(v.floatValue())
+        newCompatiblePrimitiveConverter(valueUpdater)
+
+      case DoubleType =>
+        val valueUpdater: NumericValueUpdater = (v: Number) => updater.setDouble(v.doubleValue())
+        newCompatiblePrimitiveConverter(valueUpdater)
+
+      case _ =>
+        throw new RuntimeException(
+          s"Unable to create Parquet converter for data type $catalystType " +
+            s"whose Parquet type is $parquetType. They are not compatible.")
+    }
+  }
+}
diff --git a/sql/core/src/test/scala/org/apache/spark/sql/execution/datasources/parquet/ParquetIOSuite.scala b/sql/core/src/test/scala/org/apache/spark/sql/execution/datasources/parquet/ParquetIOSuite.scala
index 3161a630af0f1..0fc3c10a2e1de 100644
--- a/sql/core/src/test/scala/org/apache/spark/sql/execution/datasources/parquet/ParquetIOSuite.scala
+++ b/sql/core/src/test/scala/org/apache/spark/sql/execution/datasources/parquet/ParquetIOSuite.scala
@@ -736,6 +736,32 @@ class ParquetIOSuite extends QueryTest with ParquetTest with SharedSQLContext {
       }
     }
   }
+
+  test("SPARK-16544 Support Parquet schema compatibility with numeric types") {
+    withSQLConf(SQLConf.PARQUET_VECTORIZED_READER_ENABLED.key -> "false") {
+      withTempPath { file =>
+        val data = (1 to 4).map(i => (i.toByte, i.toShort, i, i.toLong, i.toFloat))
+
+        spark.createDataFrame(data).toDF("a", "b", "c", "d", "e")
+          .write.parquet(file.getCanonicalPath)
+
+        val schema = StructType(
+          StructField("a", ShortType, true) ::
+          StructField("b", IntegerType, true) ::
+          StructField("c", LongType, true) ::
+          StructField("d", FloatType, true) ::
+          StructField("e", DoubleType, true) :: Nil)
+
+        val df = spark.read.schema(schema).parquet(file.getAbsolutePath)
+
+        val expectedDf = data.map { case (a, b, c, d, e) =>
+          (a.toShort, b.toInt, c.toLong, d.toFloat, e.toDouble)
+        }.toDF("a", "b", "c", "d", "e")
+
+        checkAnswer(df, expectedDf)
+      }
+    }
+  }
 }
 
 class JobCommitFailureParquetOutputCommitter(outputPath: Path, context: TaskAttemptContext)