diff --git a/libp2p/pubsub/gossipsub.py b/libp2p/pubsub/gossipsub.py
index 8613bfe8..cbed462d 100644
--- a/libp2p/pubsub/gossipsub.py
+++ b/libp2p/pubsub/gossipsub.py
@@ -10,6 +10,7 @@ from collections.abc import (
 )
 import logging
 import random
+import time
 from typing import (
     Any,
     DefaultDict,
@@ -80,8 +81,7 @@ class GossipSub(IPubsubRouter, Service):
     # The protocol peer supports
     peer_protocol: dict[ID, TProtocol]
 
-    # TODO: Add `time_since_last_publish`
-    #   Create topic --> time since last publish map.
+    time_since_last_publish: dict[str, int]
 
     mcache: MessageCache
 
@@ -138,6 +138,7 @@ class GossipSub(IPubsubRouter, Service):
             self.direct_peers[direct_peer.peer_id] = direct_peer
         self.direct_connect_interval = direct_connect_interval
         self.direct_connect_initial_delay = direct_connect_initial_delay
+        self.time_since_last_publish = {}
 
     async def run(self) -> None:
         if self.pubsub is None:
@@ -253,6 +254,8 @@ class GossipSub(IPubsubRouter, Service):
             except StreamClosed:
                 logger.debug("Fail to publish message to %s: stream closed", peer_id)
                 self.pubsub._handle_dead_peer(peer_id)
+        for topic in pubsub_msg.topicIDs:
+            self.time_since_last_publish[topic] = int(time.time())
 
     def _get_peers_to_send(
         self, topic_ids: Iterable[str], msg_forwarder: ID, origin: ID
@@ -342,6 +345,7 @@ class GossipSub(IPubsubRouter, Service):
             await self.emit_graft(topic, peer)
 
         self.fanout.pop(topic, None)
+        self.time_since_last_publish.pop(topic, None)
 
     async def leave(self, topic: str) -> None:
         # Note: the comments here are the near-exact algorithm description from the spec
@@ -514,10 +518,12 @@ class GossipSub(IPubsubRouter, Service):
 
     def fanout_heartbeat(self) -> None:
         # Note: the comments here are the exact pseudocode from the spec
-        for topic in self.fanout:
-            # Delete topic entry if it's not in `pubsub.peer_topics`
-            # or (TODO) if it's time-since-last-published > ttl
-            if topic not in self.pubsub.peer_topics:
+        for topic in list(self.fanout):
+            if (
+                topic not in self.pubsub.peer_topics
+                and self.time_since_last_publish.get(topic, 0) + self.time_to_live
+                < int(time.time())
+            ):
                 # Remove topic from fanout
                 del self.fanout[topic]
             else:
diff --git a/newsfragments/636.feature.rst b/newsfragments/636.feature.rst
new file mode 100644
index 00000000..7ec489be
--- /dev/null
+++ b/newsfragments/636.feature.rst
@@ -0,0 +1 @@
+feat: add method to compute time since last message published by a peer and remove fanout peers based on ttl.
diff --git a/tests/core/pubsub/test_gossipsub.py b/tests/core/pubsub/test_gossipsub.py
index 5e681091..20c315ef 100644
--- a/tests/core/pubsub/test_gossipsub.py
+++ b/tests/core/pubsub/test_gossipsub.py
@@ -22,13 +22,14 @@ from tests.utils.pubsub.utils import (
 @pytest.mark.trio
 async def test_join():
     async with PubsubFactory.create_batch_with_gossipsub(
-        4, degree=4, degree_low=3, degree_high=5
+        4, degree=4, degree_low=3, degree_high=5, heartbeat_interval=1, time_to_live=1
     ) as pubsubs_gsub:
         gossipsubs = [pubsub.router for pubsub in pubsubs_gsub]
         hosts = [pubsub.host for pubsub in pubsubs_gsub]
         hosts_indices = list(range(len(pubsubs_gsub)))
 
         topic = "test_join"
+        to_drop_topic = "test_drop_topic"
         central_node_index = 0
         # Remove index of central host from the indices
         hosts_indices.remove(central_node_index)
@@ -42,23 +43,31 @@ async def test_join():
         # Connect central host to all other hosts
         await one_to_all_connect(hosts, central_node_index)
 
-        # Wait 2 seconds for heartbeat to allow mesh to connect
-        await trio.sleep(2)
+        # Wait 1 seconds for heartbeat to allow mesh to connect
+        await trio.sleep(1)
 
         # Central node publish to the topic so that this topic
         # is added to central node's fanout
         # publish from the randomly chosen host
         await pubsubs_gsub[central_node_index].publish(topic, b"data")
+        await pubsubs_gsub[central_node_index].publish(to_drop_topic, b"data")
+        await trio.sleep(0.5)
+        # Check that the gossipsub of central node has fanout for the topics
+        assert topic, to_drop_topic in gossipsubs[central_node_index].fanout
+        # Check that the gossipsub of central node does not have a mesh for the topics
+        assert topic, to_drop_topic not in gossipsubs[central_node_index].mesh
+        # Check that the gossipsub of central node
+        # has a time_since_last_publish for the topics
+        assert topic in gossipsubs[central_node_index].time_since_last_publish
+        assert to_drop_topic in gossipsubs[central_node_index].time_since_last_publish
 
-        # Check that the gossipsub of central node has fanout for the topic
-        assert topic in gossipsubs[central_node_index].fanout
-        # Check that the gossipsub of central node does not have a mesh for the topic
-        assert topic not in gossipsubs[central_node_index].mesh
-
+        await trio.sleep(1)
+        # Check that after ttl the to_drop_topic is no more in fanout of central node
+        assert to_drop_topic not in gossipsubs[central_node_index].fanout
         # Central node subscribes the topic
         await pubsubs_gsub[central_node_index].subscribe(topic)
 
-        await trio.sleep(2)
+        await trio.sleep(1)
 
         # Check that the gossipsub of central node no longer has fanout for the topic
         assert topic not in gossipsubs[central_node_index].fanout