diff --git a/CHANGES/3808.bugfix b/CHANGES/3808.bugfix
new file mode 100644
index 00000000000..4691f241375
--- /dev/null
+++ b/CHANGES/3808.bugfix
@@ -0,0 +1 @@
+Reset the ``sock_read`` timeout each time data is received for a ``aiohttp.client`` response.
\ No newline at end of file
diff --git a/CONTRIBUTORS.txt b/CONTRIBUTORS.txt
index 5c63704704e..c845df4c83b 100644
--- a/CONTRIBUTORS.txt
+++ b/CONTRIBUTORS.txt
@@ -160,6 +160,7 @@ Manuel Miranda
 Marat Sharafutdinov
 Marco Paolini
 Mariano Anaya
+Martijn Pieters
 Martin Melka
 Martin Richard
 Mathias Fröjdman
diff --git a/aiohttp/client_proto.py b/aiohttp/client_proto.py
index 87db71a0e6e..a44e6454234 100644
--- a/aiohttp/client_proto.py
+++ b/aiohttp/client_proto.py
@@ -176,6 +176,8 @@ def _on_read_timeout(self) -> None:
             self._payload.set_exception(exc)
 
     def data_received(self, data: bytes) -> None:
+        self._reschedule_timeout()
+
         if not data:
             return
 
diff --git a/tests/test_client_functional.py b/tests/test_client_functional.py
index 417e1fb646c..d860663a58d 100644
--- a/tests/test_client_functional.py
+++ b/tests/test_client_functional.py
@@ -598,6 +598,56 @@ async def handler(request):
         await client.get('/')
 
 
+async def test_read_timeout_between_chunks(aiohttp_client, mocker) -> None:
+    mocker.patch('aiohttp.helpers.ceil').side_effect = ceil
+
+    async def handler(request):
+        resp = aiohttp.web.StreamResponse()
+        await resp.prepare(request)
+        # write data 4 times, with pauses. Total time 0.4 seconds.
+        for _ in range(4):
+            await asyncio.sleep(0.1)
+            await resp.write(b'data\n')
+        return resp
+
+    app = web.Application()
+    app.add_routes([web.get('/', handler)])
+
+    # A timeout of 0.2 seconds should apply per read.
+    timeout = aiohttp.ClientTimeout(sock_read=0.2)
+    client = await aiohttp_client(app, timeout=timeout)
+
+    res = b''
+    async with await client.get('/') as resp:
+        res += await resp.read()
+
+    assert res == b'data\n' * 4
+
+
+async def test_read_timeout_on_reading_chunks(aiohttp_client, mocker) -> None:
+    mocker.patch('aiohttp.helpers.ceil').side_effect = ceil
+
+    async def handler(request):
+        resp = aiohttp.web.StreamResponse()
+        await resp.prepare(request)
+        await resp.write(b'data\n')
+        await asyncio.sleep(1)
+        await resp.write(b'data\n')
+        return resp
+
+    app = web.Application()
+    app.add_routes([web.get('/', handler)])
+
+    # A timeout of 0.2 seconds should apply per read.
+    timeout = aiohttp.ClientTimeout(sock_read=0.2)
+    client = await aiohttp_client(app, timeout=timeout)
+
+    async with await client.get('/') as resp:
+        assert (await resp.content.read(5)) == b'data\n'
+        with pytest.raises(asyncio.TimeoutError):
+            await resp.content.read()
+
+
 async def test_timeout_on_reading_data(aiohttp_client, mocker) -> None:
     loop = asyncio.get_event_loop()