diff --git a/graphene/types/scalars.py b/graphene/types/scalars.py
index d4bf4675..776113e0 100644
--- a/graphene/types/scalars.py
+++ b/graphene/types/scalars.py
@@ -175,12 +175,14 @@ class OmniScalar(Scalar):
 
     _scalar_type_map = {
         str: String,
-        unicode: String,
         bool: Boolean,
         int: Int,
         float: Float,
     }
 
+    if six.PY2:
+        _scalar_type_map[unicode] = String
+
     @staticmethod
     def serialize(value):
         scalar_type = OmniScalar._scalar_type_map.get(type(value))