diff --git a/CHANGELOG.md b/CHANGELOG.md
index 4d1ff8fc..992dcff6 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -4,6 +4,10 @@ All notable changes to this project will be documented in this file.
 
 The format is based on [Keep a Changelog](https://keepachangelog.com/en/1.0.0/).
 
+## Unreleased
+
+- Handle `SSLError` exception. (#918)
+
 ## 1.0.5 (March 27th, 2024)
 
 - Handle `EndOfStream` exception for anyio backend. (#899)
diff --git a/httpcore/_backends/anyio.py b/httpcore/_backends/anyio.py
index 5731f5e7..9f4fdf86 100644
--- a/httpcore/_backends/anyio.py
+++ b/httpcore/_backends/anyio.py
@@ -64,6 +64,7 @@ async def start_tls(
             TimeoutError: ConnectTimeout,
             anyio.BrokenResourceError: ConnectError,
             anyio.EndOfStream: ConnectError,
+            ssl.SSLError: ConnectError,
         }
         with map_exceptions(exc_map):
             try: