diff --git a/CHANGELOG.md b/CHANGELOG.md
index 4c44b8ae306d..69fca9aaa49e 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -14,6 +14,7 @@
 * `[jest-util]` Fix `runOnlyPendingTimers` for `setTimeout` inside `setImmediate` ([#4608](https://github.com/facebook/jest/pull/4608))
 * `[jest-message-util]` Always remove node internals from stacktraces ([#4695](https://github.com/facebook/jest/pull/4695))
 * `[jest-resolve]` changes method of determining builtin modules to include missing builtins ([#4740](https://github.com/facebook/jest/pull/4740))
+* `[pretty-format]` Prevent error in pretty-format for window in jsdom test env ([#4750](https://github.com/facebook/jest/pull/4750))
 
 ### Features
 * `[jest-environment-*]` [**BREAKING**] Add Async Test Environment APIs, dispose is now teardown ([#4506](https://github.com/facebook/jest/pull/4506))
diff --git a/packages/pretty-format/src/__tests__/dom_element.test.js b/packages/pretty-format/src/__tests__/dom_element.test.js
index 14a00dcb30d7..2e863e0fd715 100644
--- a/packages/pretty-format/src/__tests__/dom_element.test.js
+++ b/packages/pretty-format/src/__tests__/dom_element.test.js
@@ -18,6 +18,13 @@ const toPrettyPrintTo = require('./expect_util').getPrettyPrint([DOMElement]);
 const expect: any = global.expect;
 expect.extend({toPrettyPrintTo});
 
+describe('pretty-format', () => {
+  // Test is not related to plugin but is related to jsdom testing environment.
+  it('prints global window as constructor name alone', () => {
+    expect(prettyFormat(window)).toEqual('[Window]');
+  });
+});
+
 describe('DOMElement Plugin', () => {
   it('supports a single HTML element', () => {
     expect(document.createElement('div')).toPrettyPrintTo('<div />');
diff --git a/packages/pretty-format/src/index.js b/packages/pretty-format/src/index.js
index 35a591c90da8..c1df9ac4ebcd 100644
--- a/packages/pretty-format/src/index.js
+++ b/packages/pretty-format/src/index.js
@@ -41,6 +41,10 @@ const errorToString = Error.prototype.toString;
 const regExpToString = RegExp.prototype.toString;
 const symbolToString = Symbol.prototype.toString;
 
+// Is val is equal to global window object? Works even if it does not exist :)
+/* global window */
+const isWindow = val => typeof window !== 'undefined' && val === window;
+
 const SYMBOL_REGEXP = /^Symbol\((.*)\)(.*)$/;
 const NEWLINE_REGEXP = /\n/gi;
 
@@ -224,7 +228,9 @@ function printComplexValue(
         '}';
   }
 
-  return hitMaxDepth
+  // Avoid failure to serialize global window object in jsdom test environment.
+  // For example, not even relevant if window is prop of React element.
+  return hitMaxDepth || isWindow(val)
     ? '[' + (val.constructor ? val.constructor.name : 'Object') + ']'
     : (min ? '' : (val.constructor ? val.constructor.name : 'Object') + ' ') +
       '{' +