diff --git a/CHANGES/4224.feature b/CHANGES/4224.feature
new file mode 100644
index 00000000000..a2427099b08
--- /dev/null
+++ b/CHANGES/4224.feature
@@ -0,0 +1 @@
+allow use of SameSite in cookies.
diff --git a/aiohttp/web_response.py b/aiohttp/web_response.py
index b1095b94cc0..088ce55151d 100644
--- a/aiohttp/web_response.py
+++ b/aiohttp/web_response.py
@@ -9,7 +9,7 @@
 import zlib
 from concurrent.futures import Executor
 from email.utils import parsedate
-from http.cookies import SimpleCookie
+from http.cookies import Morsel, SimpleCookie
 from typing import (  # noqa
     TYPE_CHECKING,
     Any,
@@ -27,7 +27,7 @@
 
 from . import hdrs, payload
 from .abc import AbstractStreamWriter
-from .helpers import HeadersMixin, rfc822_formatted_time, sentinel
+from .helpers import PY_38, HeadersMixin, rfc822_formatted_time, sentinel
 from .http import RESPONSES, SERVER_SOFTWARE, HttpVersion10, HttpVersion11
 from .payload import Payload
 from .typedefs import JSONEncoder, LooseHeaders
@@ -42,6 +42,12 @@
     BaseClass = collections.abc.MutableMapping
 
 
+if not PY_38:
+    # allow samesite to be used in python < 3.8
+    # already permitted in python 3.8, see https://bugs.python.org/issue29613
+    Morsel._reserved['samesite'] = 'SameSite'  # type: ignore
+
+
 class ContentCoding(enum.Enum):
     # The content codings that we have support for.
     #
@@ -183,7 +189,8 @@ def set_cookie(self, name: str, value: str, *,
                    path: str='/',
                    secure: Optional[bool]=None,
                    httponly: Optional[bool]=None,
-                   version: Optional[str]=None) -> None:
+                   version: Optional[str]=None,
+                   samesite: Optional[str]=None) -> None:
         """Set or update response cookie.
 
         Sets new cookie or updates existent with new value.
@@ -219,6 +226,8 @@ def set_cookie(self, name: str, value: str, *,
             c['httponly'] = httponly
         if version is not None:
             c['version'] = version
+        if samesite is not None:
+            c['samesite'] = samesite
 
     def del_cookie(self, name: str, *,
                    domain: Optional[str]=None,
diff --git a/docs/web_reference.rst b/docs/web_reference.rst
index 0e2263721ea..1bd55dd7f30 100644
--- a/docs/web_reference.rst
+++ b/docs/web_reference.rst
@@ -689,7 +689,8 @@ StreamResponse
 
    .. method:: set_cookie(name, value, *, path='/', expires=None, \
                           domain=None, max_age=None, \
-                          secure=None, httponly=None, version=None)
+                          secure=None, httponly=None, version=None, \
+                          samesite=None)
 
       Convenient way for setting :attr:`cookies`, allows to specify
       some additional properties like *max_age* in a single call.
@@ -734,6 +735,14 @@ StreamResponse
                           specification the cookie
                           conforms. (Optional, *version=1* by default)
 
+      :param str samesite: Asserts that a cookie must not be sent with
+         cross-origin requests, providing some protection
+         against cross-site request forgery attacks.
+         Generally the value should be one of: ``None``,
+         ``Lax`` or ``Strict``. (optional)
+
+            .. versionadded:: 3.7
+
       .. warning::
 
          In HTTP version 1.1, ``expires`` was deprecated and replaced with
diff --git a/tests/test_web_response.py b/tests/test_web_response.py
index 70eb35b769d..d269cfafc3a 100644
--- a/tests/test_web_response.py
+++ b/tests/test_web_response.py
@@ -703,13 +703,14 @@ def test_response_cookie_path() -> None:
             'Set-Cookie: name=value; expires=123; Path=/')
     resp.set_cookie('name', 'value', domain='example.com',
                     path='/home', expires='123', max_age='10',
-                    secure=True, httponly=True, version='2.0')
+                    secure=True, httponly=True, version='2.0', samesite='lax')
     assert (str(resp.cookies).lower() == 'set-cookie: name=value; '
             'domain=example.com; '
             'expires=123; '
             'httponly; '
             'max-age=10; '
             'path=/home; '
+            'samesite=lax; '
             'secure; '
             'version=2.0')