diff --git a/CHANGELOG.md b/CHANGELOG.md
index 11beba266b50..ea43cca7622f 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -31,6 +31,7 @@
 - `[jest-circus]` Fixed the issue of beforeAll & afterAll hooks getting executed even if it is inside a skipped `describe` block [#10451](https://github.com/facebook/jest/issues/10451)
 - `[jest-circus]` Fix `testLocation` on Windows when using `test.each` ([#10871](https://github.com/facebook/jest/pull/10871))
 - `[jest-cli]` Use testFailureExitCode when bailing from a failed test ([#10958](https://github.com/facebook/jest/pull/10958))
+- `[jest-cli]` Print custom error if error thrown from global hooks is not an error already ([#11003](https://github.com/facebook/jest/pull/11003))
 - `[jest-config]` [**BREAKING**] Change default file extension order by moving json behind ts and tsx ([10572](https://github.com/facebook/jest/pull/10572))
 - `[jest-console]` `console.dir` now respects the second argument correctly ([#10638](https://github.com/facebook/jest/pull/10638))
 - `[jest-each]` [**BREAKING**] Ignore excess words in headings ([#8766](https://github.com/facebook/jest/pull/8766))
diff --git a/e2e/__tests__/globalSetup.test.ts b/e2e/__tests__/globalSetup.test.ts
index a7b993b4ba84..04e08bd4fa0d 100644
--- a/e2e/__tests__/globalSetup.test.ts
+++ b/e2e/__tests__/globalSetup.test.ts
@@ -8,7 +8,12 @@
 import {tmpdir} from 'os';
 import * as path from 'path';
 import * as fs from 'graceful-fs';
-import {cleanup, runYarnInstall} from '../Utils';
+import {
+  cleanup,
+  createEmptyPackage,
+  runYarnInstall,
+  writeFiles,
+} from '../Utils';
 import runJest, {json as runWithJson} from '../runJest';
 
 const DIR = path.join(tmpdir(), 'jest-global-setup');
@@ -19,6 +24,7 @@ const customTransformDIR = path.join(
   'jest-global-setup-custom-transform',
 );
 const nodeModulesDIR = path.join(tmpdir(), 'jest-global-setup-node-modules');
+const rejectionDir = path.join(tmpdir(), 'jest-global-setup-rejection');
 const e2eDir = path.resolve(__dirname, '../global-setup');
 
 beforeAll(() => {
@@ -31,13 +37,16 @@ beforeEach(() => {
   cleanup(project2DIR);
   cleanup(customTransformDIR);
   cleanup(nodeModulesDIR);
+  cleanup(rejectionDir);
 });
+
 afterAll(() => {
   cleanup(DIR);
   cleanup(project1DIR);
   cleanup(project2DIR);
   cleanup(customTransformDIR);
   cleanup(nodeModulesDIR);
+  cleanup(rejectionDir);
 });
 
 test('globalSetup is triggered once before all test suites', () => {
@@ -62,8 +71,9 @@ test('jest throws an error when globalSetup does not export a function', () => {
   ]);
 
   expect(exitCode).toBe(1);
-  expect(stderr).toMatch(
-    `TypeError: globalSetup file must export a function at ${setupPath}`,
+  expect(stderr).toContain('Jest: Got error running globalSetup');
+  expect(stderr).toContain(
+    `globalSetup file must export a function at ${setupPath}`,
   );
 });
 
@@ -145,8 +155,9 @@ test('globalSetup throws with named export', () => {
   ]);
 
   expect(exitCode).toBe(1);
-  expect(stderr).toMatch(
-    `TypeError: globalSetup file must export a function at ${setupPath}`,
+  expect(stderr).toContain('Jest: Got error running globalSetup');
+  expect(stderr).toContain(
+    `globalSetup file must export a function at ${setupPath}`,
   );
 });
 
@@ -161,3 +172,23 @@ test('should transform node_modules if configured by transformIgnorePatterns', (
 
   expect(exitCode).toBe(0);
 });
+
+test('properly handle rejections', () => {
+  createEmptyPackage(rejectionDir, {jest: {globalSetup: '<rootDir>/setup.js'}});
+  writeFiles(rejectionDir, {
+    'setup.js': `
+      module.exports = () => Promise.reject();
+    `,
+    'test.js': `
+      test('dummy', () => {
+        expect(true).toBe(true);
+      });
+    `,
+  });
+
+  const {exitCode, stderr} = runJest(rejectionDir, [`--no-cache`]);
+
+  expect(exitCode).toBe(1);
+  expect(stderr).toContain('Error: Jest: Got error running globalSetup');
+  expect(stderr).toContain('reason: undefined');
+});
diff --git a/e2e/__tests__/globalTeardown.test.ts b/e2e/__tests__/globalTeardown.test.ts
index a3947ef1c337..200faff130f4 100644
--- a/e2e/__tests__/globalTeardown.test.ts
+++ b/e2e/__tests__/globalTeardown.test.ts
@@ -55,8 +55,9 @@ test('jest throws an error when globalTeardown does not export a function', () =
   ]);
 
   expect(exitCode).toBe(1);
-  expect(stderr).toMatch(
-    `TypeError: globalTeardown file must export a function at ${teardownPath}`,
+  expect(stderr).toContain('Jest: Got error running globalTeardown');
+  expect(stderr).toContain(
+    `globalTeardown file must export a function at ${teardownPath}`,
   );
 });
 
@@ -125,7 +126,8 @@ test('globalTeardown throws with named export', () => {
   ]);
 
   expect(exitCode).toBe(1);
-  expect(stderr).toMatch(
-    `TypeError: globalTeardown file must export a function at ${teardownPath}`,
+  expect(stderr).toContain('Jest: Got error running globalTeardown');
+  expect(stderr).toContain(
+    `globalTeardown file must export a function at ${teardownPath}`,
   );
 });
diff --git a/packages/jest-cli/src/cli/index.ts b/packages/jest-cli/src/cli/index.ts
index a20eae54d50d..8290539785d6 100644
--- a/packages/jest-cli/src/cli/index.ts
+++ b/packages/jest-cli/src/cli/index.ts
@@ -37,7 +37,7 @@ export async function run(
   } catch (error) {
     clearLine(process.stderr);
     clearLine(process.stdout);
-    if (error.stack) {
+    if (error?.stack) {
       console.error(chalk.red(error.stack));
     } else {
       console.error(chalk.red(error));
diff --git a/packages/jest-core/src/runGlobalHook.ts b/packages/jest-core/src/runGlobalHook.ts
index c6779becf80e..82dc3a5c1071 100644
--- a/packages/jest-core/src/runGlobalHook.ts
+++ b/packages/jest-core/src/runGlobalHook.ts
@@ -5,11 +5,13 @@
  * LICENSE file in the root directory of this source tree.
  */
 
+import * as util from 'util';
 import pEachSeries = require('p-each-series');
 import {ScriptTransformer} from '@jest/transform';
 import type {Config} from '@jest/types';
 import type {Test} from 'jest-runner';
 import {interopRequireDefault} from 'jest-util';
+import prettyFormat from 'pretty-format';
 
 export default async ({
   allTests,
@@ -29,7 +31,7 @@ export default async ({
   }
 
   if (globalModulePaths.size > 0) {
-    await pEachSeries(Array.from(globalModulePaths), async modulePath => {
+    await pEachSeries(globalModulePaths, async modulePath => {
       if (!modulePath) {
         return;
       }
@@ -45,17 +47,32 @@ export default async ({
 
       const transformer = new ScriptTransformer(projectConfig);
 
-      await transformer.requireAndTranspileModule(modulePath, async m => {
-        const globalModule = interopRequireDefault(m).default;
+      try {
+        await transformer.requireAndTranspileModule(modulePath, async m => {
+          const globalModule = interopRequireDefault(m).default;
 
-        if (typeof globalModule !== 'function') {
-          throw new TypeError(
-            `${moduleName} file must export a function at ${modulePath}`,
-          );
+          if (typeof globalModule !== 'function') {
+            throw new TypeError(
+              `${moduleName} file must export a function at ${modulePath}`,
+            );
+          }
+
+          await globalModule(globalConfig);
+        });
+      } catch (error) {
+        if (util.types.isNativeError(error)) {
+          error.message = `Jest: Got error running ${moduleName} - ${modulePath}, reason: ${error.message}`;
+
+          throw error;
         }
 
-        await globalModule(globalConfig);
-      });
+        throw new Error(
+          `Jest: Got error running ${moduleName} - ${modulePath}, reason: ${prettyFormat(
+            error,
+            {maxDepth: 3},
+          )}`,
+        );
+      }
     });
   }