diff --git a/jedi/evaluate/pep0484.py b/jedi/evaluate/pep0484.py
index 536e624b..a9dc748c 100644
--- a/jedi/evaluate/pep0484.py
+++ b/jedi/evaluate/pep0484.py
@@ -7,8 +7,8 @@ as annotations in future python versions.
 The (initial / probably incomplete) implementation todo list for pep-0484:
 v Function parameter annotations with builtin/custom type classes
 v Function returntype annotations with builtin/custom type classes
-x Function parameter annotations with strings (forward reference)
-x Function return type annotations with strings (forward reference)
+v Function parameter annotations with strings (forward reference)
+v Function return type annotations with strings (forward reference)
 x Local variable type hints
 x Assigned types: `Url = str\ndef get(url:Url) -> str:`
 x Type hints in `with` statements
diff --git a/jedi/parser/tree.py b/jedi/parser/tree.py
index c5fb0934..df116820 100644
--- a/jedi/parser/tree.py
+++ b/jedi/parser/tree.py
@@ -41,6 +41,7 @@ import textwrap
 from jedi._compatibility import (Python3Method, encoding, is_py3, utf8_repr,
                                  literal_eval, use_metaclass, unicode)
 from jedi import cache
+import ast
 
 
 def is_node(node, *symbol_names):
@@ -52,6 +53,19 @@ def is_node(node, *symbol_names):
         return type in symbol_names
 
 
+def _fix_forward_reference(annotation):
+    if isinstance(annotation, String):
+        newannotation = Name(
+            annotation.position_modifier,
+            ast.literal_eval(annotation.value),
+            annotation.start_pos,
+            annotation.prefix)
+        newannotation.parent = annotation.parent
+    else:
+        newannotation = annotation
+    return newannotation
+
+
 class PositionModifier(object):
     """A start_pos modifier for the fast parser."""
     def __init__(self):
@@ -865,9 +879,12 @@ class Function(ClassOrFunc):
         return bool(self.yields)
 
     def annotation(self):
+        if self.children[0] == "lambda":
+            # lambda functions have no annotation
+            return None
         try:
             if self.children[3] == "->":
-                return self.children[4]
+                return _fix_forward_reference(self.children[4])
             assert self.children[3] == ":"
         except IndexError:
             return None
@@ -1409,7 +1426,8 @@ class Param(BaseNode):
         if is_node(tfpdef, 'tfpdef'):
             assert tfpdef.children[1] == ":"
             assert len(tfpdef.children) == 3
-            return tfpdef.children[2]
+            annotation = tfpdef.children[2]
+            return _fix_forward_reference(annotation)
         else:
             return None
 
diff --git a/test/completion/pep0484.py b/test/completion/pep0484.py
index 52550405..6a7ce6ce 100644
--- a/test/completion/pep0484.py
+++ b/test/completion/pep0484.py
@@ -68,3 +68,23 @@ def return_annotation_and_docstring_different() -> str:
 
 #? str()
 return_annotation_and_docstring_different()
+
+
+def annotation_forward_reference(b: "B") -> "B":
+    #? B()
+    b
+
+#? B()
+annotation_forward_reference(1)
+
+class B:
+    pass
+
+
+class SelfReference:
+    def test(x: "SelfReference") -> "SelfReference":
+        #? SelfReference()
+        x
+
+#? SelfReference()
+SelfReference().test()