diff --git a/pyflakes/checker.py b/pyflakes/checker.py
index d8f093a1..a0708222 100644
--- a/pyflakes/checker.py
+++ b/pyflakes/checker.py
@@ -922,6 +922,39 @@ def handleDoctests(self, node):
         self.popScope()
         self.scopeStack = saved_stack
 
+    def handleAnnotation(self, annotation, node):
+        if isinstance(annotation, ast.Str):
+            # Defer handling forward annotation.
+            def handleForwardAnnotation():
+                try:
+                    tree = ast.parse(annotation.s)
+                except SyntaxError:
+                    self.report(
+                        messages.ForwardAnnotationSyntaxError,
+                        node,
+                        annotation.s,
+                    )
+                    return
+
+                body = tree.body
+                if len(body) != 1 or not isinstance(body[0], ast.Expr):
+                    self.report(
+                        messages.ForwardAnnotationSyntaxError,
+                        node,
+                        annotation.s,
+                    )
+                    return
+
+                parsed_annotation = tree.body[0].value
+                for descendant in ast.walk(parsed_annotation):
+                    ast.copy_location(descendant, annotation)
+
+                self.handleNode(parsed_annotation, node)
+
+            self.deferFunction(handleForwardAnnotation)
+        else:
+            self.handleNode(annotation, node)
+
     def ignore(self, node):
         pass
 
@@ -1160,9 +1193,11 @@ def addArgs(arglist):
                 if arg in args[:idx]:
                     self.report(messages.DuplicateArgument, node, arg)
 
-        for child in annotations + defaults:
-            if child:
-                self.handleNode(child, node)
+        for annotation in annotations:
+            self.handleAnnotation(annotation, node)
+
+        for default in defaults:
+            self.handleNode(default, node)
 
         def runFunction():
 
@@ -1375,7 +1410,7 @@ def ANNASSIGN(self, node):
             # Otherwise it's not really ast.Store and shouldn't silence
             # UndefinedLocal warnings.
             self.handleNode(node.target, node)
-        self.handleNode(node.annotation, node)
+        self.handleAnnotation(node.annotation, node)
         if node.value:
             # If the assignment has value, handle the *value* now.
             self.handleNode(node.value, node)
diff --git a/pyflakes/messages.py b/pyflakes/messages.py
index 9e9406c3..670f95f6 100644
--- a/pyflakes/messages.py
+++ b/pyflakes/messages.py
@@ -231,3 +231,11 @@ class AssertTuple(Message):
     Assertion test is a tuple, which are always True.
     """
     message = 'assertion is always true, perhaps remove parentheses?'
+
+
+class ForwardAnnotationSyntaxError(Message):
+    message = 'syntax error in forward annotation %r'
+
+    def __init__(self, filename, loc, annotation):
+        Message.__init__(self, filename, loc)
+        self.message_args = (annotation,)
diff --git a/pyflakes/test/test_other.py b/pyflakes/test/test_other.py
index ba052f18..14f213c4 100644
--- a/pyflakes/test/test_other.py
+++ b/pyflakes/test/test_other.py
@@ -1890,3 +1890,77 @@ def f():
             class C:
                 foo: not_a_real_type = None
         ''', m.UndefinedName)
+        self.flakes('''
+        from foo import Bar
+        bar: Bar
+        ''')
+        self.flakes('''
+        from foo import Bar
+        bar: 'Bar'
+        ''')
+        self.flakes('''
+        import foo
+        bar: foo.Bar
+        ''')
+        self.flakes('''
+        import foo
+        bar: 'foo.Bar'
+        ''')
+        self.flakes('''
+        from foo import Bar
+        def f(bar: Bar): pass
+        ''')
+        self.flakes('''
+        from foo import Bar
+        def f(bar: 'Bar'): pass
+        ''')
+        self.flakes('''
+        from foo import Bar
+        def f(bar) -> Bar: return bar
+        ''')
+        self.flakes('''
+        from foo import Bar
+        def f(bar) -> 'Bar': return bar
+        ''')
+        self.flakes('''
+        bar: 'Bar'
+        ''', m.UndefinedName)
+        self.flakes('''
+        bar: 'foo.Bar'
+        ''', m.UndefinedName)
+        self.flakes('''
+        from foo import Bar
+        bar: str
+        ''', m.UnusedImport)
+        self.flakes('''
+        from foo import Bar
+        def f(bar: str): pass
+        ''', m.UnusedImport)
+        self.flakes('''
+        def f(a: A) -> A: pass
+        class A: pass
+        ''', m.UndefinedName, m.UndefinedName)
+        self.flakes('''
+        def f(a: 'A') -> 'A': return a
+        class A: pass
+        ''')
+        self.flakes('''
+        a: A
+        class A: pass
+        ''', m.UndefinedName)
+        self.flakes('''
+        a: 'A'
+        class A: pass
+        ''')
+        self.flakes('''
+        a: 'A B'
+        ''', m.ForwardAnnotationSyntaxError)
+        self.flakes('''
+        a: 'A; B'
+        ''', m.ForwardAnnotationSyntaxError)
+        self.flakes('''
+        a: '1 + 2'
+        ''')
+        self.flakes('''
+        a: 'a: "A"'
+        ''', m.ForwardAnnotationSyntaxError)