diff --git a/docs/responses.md b/docs/responses.md
index 595c9101c..9aaf24e1f 100644
--- a/docs/responses.md
+++ b/docs/responses.md
@@ -154,7 +154,7 @@ class App:
 
 ### StreamingResponse
 
-Takes an async generator and streams the response body.
+Takes an async generator or a normal generator/iterator and streams the response body.
 
 ```python
 from starlette.responses import StreamingResponse
@@ -180,6 +180,8 @@ class App:
         await response(receive, send)
 ```
 
+Have in mind that <a href="https://docs.python.org/3/glossary.html#term-file-like-object" target="_blank">file-like</a> objects (like those created by `open()`) are normal iterators. So, you can return them directly in a `StreamingResponse`.
+
 ### FileResponse
 
 Asynchronously streams a file as the response.
diff --git a/starlette/concurrency.py b/starlette/concurrency.py
index 35b589956..dd9860aaf 100644
--- a/starlette/concurrency.py
+++ b/starlette/concurrency.py
@@ -1,6 +1,7 @@
 import asyncio
 import functools
 import typing
+from typing import Any, AsyncGenerator, Iterator
 
 try:
     import contextvars  # Python 3.7+ only.
@@ -22,3 +23,24 @@ async def run_in_threadpool(
         # loop.run_in_executor doesn't accept 'kwargs', so bind them in here
         func = functools.partial(func, **kwargs)
     return await loop.run_in_executor(None, func, *args)
+
+
+class _StopSyncIteration(Exception):
+    pass
+
+
+def _interceptable_next(iterator: Iterator) -> Any:
+    try:
+        result = next(iterator)
+        return result
+    except StopIteration:
+        raise _StopSyncIteration
+
+
+async def iterate_in_threadpool(iterator: Iterator) -> AsyncGenerator:
+    while True:
+        try:
+            result = await run_in_threadpool(_interceptable_next, iterator)
+            yield result
+        except _StopSyncIteration:
+            break
diff --git a/starlette/responses.py b/starlette/responses.py
index 1fee57cc0..48afc47ad 100644
--- a/starlette/responses.py
+++ b/starlette/responses.py
@@ -1,5 +1,6 @@
 import hashlib
 import http.cookies
+import inspect
 import json
 import os
 import stat
@@ -9,6 +10,7 @@
 from urllib.parse import quote_plus
 
 from starlette.background import BackgroundTask
+from starlette.concurrency import iterate_in_threadpool
 from starlette.datastructures import URL, MutableHeaders
 from starlette.types import Receive, Scope, Send
 
@@ -175,7 +177,10 @@ def __init__(
         media_type: str = None,
         background: BackgroundTask = None,
     ) -> None:
-        self.body_iterator = content
+        if inspect.isasyncgen(content):
+            self.body_iterator = content
+        else:
+            self.body_iterator = iterate_in_threadpool(content)
         self.status_code = status_code
         self.media_type = self.media_type if media_type is None else media_type
         self.background = background
diff --git a/tests/test_responses.py b/tests/test_responses.py
index 300975afe..3d5de413f 100644
--- a/tests/test_responses.py
+++ b/tests/test_responses.py
@@ -90,6 +90,23 @@ async def numbers_for_cleanup(start=1, stop=5):
     assert filled_by_bg_task == "6, 7, 8, 9"
 
 
+def test_sync_streaming_response():
+    async def app(scope, receive, send):
+        def numbers(minimum, maximum):
+            for i in range(minimum, maximum + 1):
+                yield str(i)
+                if i != maximum:
+                    yield ", "
+
+        generator = numbers(1, 5)
+        response = StreamingResponse(generator, media_type="text/plain")
+        await response(scope, receive, send)
+
+    client = TestClient(app)
+    response = client.get("/")
+    assert response.text == "1, 2, 3, 4, 5"
+
+
 def test_response_headers():
     async def app(scope, receive, send):
         headers = {"x-header-1": "123", "x-header-2": "456"}