diff --git a/docs/routing.md b/docs/routing.md
index 3489880a4..a08463d12 100644
--- a/docs/routing.md
+++ b/docs/routing.md
@@ -43,6 +43,7 @@ You can use convertors to modify what is captured. Four convertors are available
 * `str` returns a string, and is the default.
 * `int` returns a Python integer.
 * `float` returns a Python float.
+* `uuid` return a Python `uuid.UUID` instance.
 * `path` returns the rest of the path, including any additional `/` characers.
 
 Convertors are used by prefixing them with a colon, like so:
diff --git a/starlette/convertors.py b/starlette/convertors.py
index acbc03a3c..7afe4c8d1 100644
--- a/starlette/convertors.py
+++ b/starlette/convertors.py
@@ -1,5 +1,6 @@
 import math
 import typing
+import uuid
 
 
 class Convertor:
@@ -61,9 +62,20 @@ def to_string(self, value: typing.Any) -> str:
         return ("%0.20f" % value).rstrip("0").rstrip(".")
 
 
+class UUIDConvertor(Convertor):
+    regex = "[0-9a-f]{8}-[0-9a-f]{4}-[0-9a-f]{4}-[0-9a-f]{4}-[0-9a-f]{12}"
+
+    def convert(self, value: str) -> typing.Any:
+        return uuid.UUID(value)
+
+    def to_string(self, value: typing.Any) -> str:
+        return str(value)
+
+
 CONVERTOR_TYPES = {
     "str": StringConvertor(),
     "path": PathConvertor(),
     "int": IntegerConvertor(),
     "float": FloatConvertor(),
+    "uuid": UUIDConvertor(),
 }
diff --git a/tests/test_routing.py b/tests/test_routing.py
index e3de089b9..2a7e6c244 100644
--- a/tests/test_routing.py
+++ b/tests/test_routing.py
@@ -1,3 +1,5 @@
+import uuid
+
 import pytest
 
 from starlette.applications import Starlette
@@ -75,6 +77,12 @@ def path_convertor(request):
     return JSONResponse({"path": path})
 
 
+@app.route("/uuid/{param:uuid}", name="uuid-convertor")
+def uuid_converter(request):
+    uuid_param = request.path_params["param"]
+    return JSONResponse({"uuid": str(uuid_param)})
+
+
 @app.websocket_route("/ws")
 async def websocket_endpoint(session):
     await session.accept()
@@ -152,6 +160,17 @@ def test_route_converters():
         app.url_path_for("path-convertor", param="some/example") == "/path/some/example"
     )
 
+    # Test UUID conversion
+    response = client.get("/uuid/ec38df32-ceda-4cfa-9b4a-1aeb94ad551a")
+    assert response.status_code == 200
+    assert response.json() == {"uuid": "ec38df32-ceda-4cfa-9b4a-1aeb94ad551a"}
+    assert (
+        app.url_path_for(
+            "uuid-convertor", param=uuid.UUID("ec38df32-ceda-4cfa-9b4a-1aeb94ad551a")
+        )
+        == "/uuid/ec38df32-ceda-4cfa-9b4a-1aeb94ad551a"
+    )
+
 
 def test_url_path_for():
     assert app.url_path_for("homepage") == "/"