diff --git a/jedi/evaluate/finder.py b/jedi/evaluate/finder.py
index 89de08e4..ad2a6c33 100644
--- a/jedi/evaluate/finder.py
+++ b/jedi/evaluate/finder.py
@@ -23,6 +23,7 @@ from jedi.evaluate import representation as er
 from jedi.evaluate import dynamic
 from jedi.evaluate import compiled
 from jedi.evaluate import docstrings
+from jedi.evaluate import pep0484
 from jedi.evaluate import iterable
 from jedi.evaluate import imports
 from jedi.evaluate import analysis
@@ -387,6 +388,11 @@ def _eval_param(evaluator, param, scope):
             and func.instance.is_generated and str(func.name) == '__init__':
         param = func.var.params[param.position_nr]
 
+    # Add pep0484 type hints
+    pep0484_hints = pep0484.follow_param(evaluator, param)
+    if pep0484_hints:
+        return pep0484_hints
+
     # Add docstring knowledge.
     doc_params = docstrings.follow_param(evaluator, param)
     if doc_params:
diff --git a/jedi/evaluate/pep0484.py b/jedi/evaluate/pep0484.py
new file mode 100644
index 00000000..97433502
--- /dev/null
+++ b/jedi/evaluate/pep0484.py
@@ -0,0 +1,34 @@
+"""
+PEP 0484 ( https://www.python.org/dev/peps/pep-0484/ ) describes type hints
+through function annotations. There is a strong suggestion in this document
+that only the type of type hinting defined in PEP0484 should be allowed
+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
+x 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)
+x Local variable type hints
+x Assigned types: `Url = str\ndef get(url:Url) -> str:`
+x Type hints in `with` statements
+x Stub files support
+"""
+
+from itertools import chain
+
+from jedi.evaluate.cache import memoize_default
+
+
+@memoize_default(None, evaluator_is_first_arg=True)
+def follow_param(evaluator, param):
+    # annotation is in param.children[0] if present
+    # either this firstchild is a Name (if no annotation is present) or a Node
+    if hasattr(param.children[0], "children"):
+        assert len(param.children[0].children) == 3 and \
+            param.children[0].children[1] == ":"
+        definitions = evaluator.eval_element(param.children[0].children[2])
+        return list(chain.from_iterable(
+            evaluator.execute(d) for d in definitions))
+    else:
+        return []
diff --git a/test/completion/pep0484.py b/test/completion/pep0484.py
new file mode 100644
index 00000000..dac4f17a
--- /dev/null
+++ b/test/completion/pep0484.py
@@ -0,0 +1,14 @@
+""" Pep-0484 type hinting """
+
+# -----------------
+# sphinx style
+# -----------------
+def typehints(a, b: str, c: int, d:int = 4):
+    #? 
+    a
+    #? str()
+    b
+    #? int()
+    c
+    #? int()
+    d