diff --git a/src/net_processing.cpp b/src/net_processing.cpp
--- a/src/net_processing.cpp
+++ b/src/net_processing.cpp
@@ -2287,9 +2287,17 @@
                  pfrom->nStartingHeight, addrMe.ToString(), pfrom->GetId(),
                  remoteAddr);
 
-        int64_t nTimeOffset = nTime - GetTime();
-        pfrom->nTimeOffset = nTimeOffset;
-        AddTimeData(pfrom->addr, nTimeOffset);
+        // Ignore time offsets that are improbable (before the Genesis block)
+        // and may underflow the nTimeOffset calculation.
+        int64_t currentTime = GetTime();
+        if (nTime >= int64_t(chainparams.GenesisBlock().nTime)) {
+            int64_t nTimeOffset = nTime - currentTime;
+            pfrom->nTimeOffset = nTimeOffset;
+            AddTimeData(pfrom->addr, nTimeOffset);
+        } else {
+            Misbehaving(pfrom, 20,
+                        "Ignoring invalid timestamp in version message");
+        }
 
         // Feeler connections exist only to verify if address is online.
         if (pfrom->fFeeler) {
diff --git a/test/functional/abc-version-message.py b/test/functional/abc-version-message.py
new file mode 100755
--- /dev/null
+++ b/test/functional/abc-version-message.py
@@ -0,0 +1,59 @@
+#!/usr/bin/env python3
+# Copyright (c) 2020 The Bitcoin developers
+# Distributed under the MIT software license, see the accompanying
+# file COPYING or http://www.opensource.org/licenses/mit-license.php.
+"""Test version message behavior"""
+
+from test_framework.messages import NODE_NETWORK, msg_version
+from test_framework.mininode import P2PInterface
+from test_framework.test_framework import BitcoinTestFramework
+
+
+class ModifiedVersionTimestampP2PInterface(P2PInterface):
+    def __init__(self, timestamp):
+        super().__init__()
+        self.versionTimestamp = timestamp
+
+    def peer_connect(self, *args, services=NODE_NETWORK,
+                     send_version=False, **kwargs):
+        create_conn = super().peer_connect(*args, send_version=send_version, **kwargs)
+
+        # Send version message with invalid timestamp
+        vt = msg_version()
+        vt.nTime = self.versionTimestamp
+
+        vt.nServices = services
+        vt.addrTo.ip = self.dstaddr
+        vt.addrTo.port = self.dstport
+        vt.addrFrom.ip = "0.0.0.0"
+        vt.addrFrom.port = 0
+
+        # Will be sent right after connection_made
+        self.on_connection_send_msg = vt
+        return create_conn
+
+
+class VersionMessageTest(BitcoinTestFramework):
+    def set_test_params(self):
+        self.num_nodes = 1
+        self.setup_clean_chain = False
+
+    def run_test(self):
+        # Check some invalid timestamps in the version message
+        with self.nodes[0].assert_debug_log(expected_msgs=["Ignoring invalid timestamp in version message"]):
+            self.nodes[0].add_p2p_connection(
+                ModifiedVersionTimestampP2PInterface(-9223372036854775807), send_version=False)
+
+        # Check timestamp boundary
+        with self.nodes[0].assert_debug_log(expected_msgs=["Ignoring invalid timestamp in version message"]):
+            self.nodes[0].add_p2p_connection(
+                ModifiedVersionTimestampP2PInterface(1296688601), send_version=False)
+
+        # Genesis block timestamp
+        with self.nodes[0].assert_debug_log(expected_msgs=["added time data"], unexpected_msgs=["Ignoring invalid timestamp in version message"]):
+            self.nodes[0].add_p2p_connection(
+                ModifiedVersionTimestampP2PInterface(1296688602), send_version=False)
+
+
+if __name__ == '__main__':
+    VersionMessageTest().main()