diff --git a/src/rules/requireReturnType.js b/src/rules/requireReturnType.js
index be70988c..450647f3 100644
--- a/src/rules/requireReturnType.js
+++ b/src/rules/requireReturnType.js
@@ -59,8 +59,14 @@ const create = (context) => {
   const getIsReturnTypeAnnotationUndefined = (targetNode) => {
     const isReturnTypeAnnotationLiteralUndefined = _.get(targetNode, 'functionNode.returnType.typeAnnotation.id.name') === 'undefined' && _.get(targetNode, 'functionNode.returnType.typeAnnotation.type') === 'GenericTypeAnnotation';
     const isReturnTypeAnnotationVoid = _.get(targetNode, 'functionNode.returnType.typeAnnotation.type') === 'VoidTypeAnnotation';
-
-    return isReturnTypeAnnotationLiteralUndefined || isReturnTypeAnnotationVoid;
+    const isAsyncReturnTypeAnnotationVoid = _.get(targetNode, 'functionNode.async') &&
+      _.get(targetNode, 'functionNode.returnType.typeAnnotation.id.name') === 'Promise' && (
+      _.get(targetNode, 'functionNode.returnType.typeAnnotation.typeParameters.params[0].type') === 'VoidTypeAnnotation' ||
+      _.get(targetNode, 'functionNode.returnType.typeAnnotation.typeParameters.params[0].id.name') === 'undefined' &&
+      _.get(targetNode, 'functionNode.returnType.typeAnnotation.typeParameters.params[0].type') === 'GenericTypeAnnotation'
+    );
+
+    return isReturnTypeAnnotationLiteralUndefined || isReturnTypeAnnotationVoid || isAsyncReturnTypeAnnotationVoid;
   };
 
   const shouldFilterNode = (functionNode) => {
@@ -102,8 +108,7 @@ const create = (context) => {
 
     const isArrow = functionNode.type === 'ArrowFunctionExpression';
     const isArrowFunctionExpression = functionNode.expression;
-    const hasImplicitReturnType = functionNode.async || functionNode.generator;
-    const isFunctionReturnUndefined = !isArrowFunctionExpression && !hasImplicitReturnType && (!targetNode.returnStatementNode || isUndefinedReturnType(targetNode.returnStatementNode));
+    const isFunctionReturnUndefined = !isArrowFunctionExpression && !(functionNode.generator && !functionNode.async) && (!targetNode.returnStatementNode || isUndefinedReturnType(targetNode.returnStatementNode));
     const isReturnTypeAnnotationUndefined = getIsReturnTypeAnnotationUndefined(targetNode);
 
     if (skipArrows === 'expressionsOnly' && isArrowFunctionExpression || skipArrows === true && isArrow) {
diff --git a/tests/rules/assertions/requireReturnType.js b/tests/rules/assertions/requireReturnType.js
index 07e2bbf4..40e3ec7f 100644
--- a/tests/rules/assertions/requireReturnType.js
+++ b/tests/rules/assertions/requireReturnType.js
@@ -201,7 +201,7 @@ export default {
       code: 'async () => {}',
       errors: [
         {
-          message: 'Missing return type annotation.'
+          message: 'Must annotate undefined return type.'
         }
       ],
       options: [
@@ -215,7 +215,7 @@ export default {
       code: 'async function x() {}',
       errors: [
         {
-          message: 'Missing return type annotation.'
+          message: 'Must annotate undefined return type.'
         }
       ],
       options: [
@@ -226,29 +226,49 @@ export default {
       ]
     },
     {
-      code: 'class Test { constructor() { } }',
+      code: 'async (): Promise<void> => { return; }',
       errors: [
         {
-          message: 'Must annotate undefined return type.'
+          message: 'Must not annotate undefined return type.'
         }
       ],
       options: [
         'always',
         {
-          annotateUndefined: 'always'
+          annotateUndefined: 'never'
         }
       ]
     },
     {
-      code: 'class Test { foo() { return 42; } }',
+      code: 'async (): Promise<undefined> => { return; }',
       errors: [
         {
-          message: 'Missing return type annotation.'
+          message: 'Must not annotate undefined return type.'
+        }
+      ],
+      options: [
+        'always',
+        {
+          annotateUndefined: 'never'
         }
       ]
     },
     {
-      code: 'class Test { foo = () => { return 42; } }',
+      code: 'class Test { constructor() { } }',
+      errors: [
+        {
+          message: 'Must annotate undefined return type.'
+        }
+      ],
+      options: [
+        'always',
+        {
+          annotateUndefined: 'always'
+        }
+      ]
+    },
+    {
+      code: 'class Test { foo() { return 42; } }',
       errors: [
         {
           message: 'Missing return type annotation.'
@@ -256,7 +276,7 @@ export default {
       ]
     },
     {
-      code: 'class Test { foo = () => 42; }',
+      code: 'class Test { foo = () => { return 42; } }',
       errors: [
         {
           message: 'Missing return type annotation.'
@@ -264,14 +284,11 @@ export default {
       ]
     },
     {
-      code: 'async () => { return; }',
+      code: 'class Test { foo = () => 42; }',
       errors: [
         {
           message: 'Missing return type annotation.'
         }
-      ],
-      options: [
-        'always'
       ]
     },
     {