diff --git a/CHANGELOG.md b/CHANGELOG.md
index f63110425..cc2ec746c 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
+
+- Added httpcore.SSLError and redirect TLS handshake errors to it. (#960)
+
 ## Version 1.0.6 (October 1st, 2024)
 
 - Relax `trio` dependency pinning. (#956)
diff --git a/docs/exceptions.md b/docs/exceptions.md
index 63ef3f28e..3d01dd057 100644
--- a/docs/exceptions.md
+++ b/docs/exceptions.md
@@ -9,6 +9,7 @@ The following exceptions may be raised when sending a request:
     * `httpcore.WriteTimeout`
 * `httpcore.NetworkError`
     * `httpcore.ConnectError`
+        * `httpcore.SSLError`
     * `httpcore.ReadError`
     * `httpcore.WriteError`
 * `httpcore.ProtocolError`
diff --git a/httpcore/__init__.py b/httpcore/__init__.py
index 330745a5d..5d2a1e601 100644
--- a/httpcore/__init__.py
+++ b/httpcore/__init__.py
@@ -29,6 +29,7 @@
     ReadError,
     ReadTimeout,
     RemoteProtocolError,
+    SSLError,
     TimeoutException,
     UnsupportedProtocol,
     WriteError,
@@ -128,6 +129,7 @@ def __init__(self, *args, **kwargs):  # type: ignore
     "ConnectError",
     "ReadError",
     "WriteError",
+    "SSLError",
 ]
 
 __version__ = "1.0.6"
diff --git a/httpcore/_backends/anyio.py b/httpcore/_backends/anyio.py
index d469e0084..66d552e7f 100644
--- a/httpcore/_backends/anyio.py
+++ b/httpcore/_backends/anyio.py
@@ -8,6 +8,7 @@
     ConnectTimeout,
     ReadError,
     ReadTimeout,
+    SSLError,
     WriteError,
     WriteTimeout,
     map_exceptions,
@@ -64,7 +65,7 @@ async def start_tls(
             TimeoutError: ConnectTimeout,
             anyio.BrokenResourceError: ConnectError,
             anyio.EndOfStream: ConnectError,
-            ssl.SSLError: ConnectError,
+            ssl.SSLError: SSLError,
         }
         with map_exceptions(exc_map):
             try:
diff --git a/httpcore/_exceptions.py b/httpcore/_exceptions.py
index 81e7fc61d..e0f60fa5f 100644
--- a/httpcore/_exceptions.py
+++ b/httpcore/_exceptions.py
@@ -1,4 +1,5 @@
 import contextlib
+import ssl
 from typing import Iterator, Mapping, Type
 
 ExceptionMapping = Mapping[Type[Exception], Type[Exception]]
@@ -79,3 +80,7 @@ class ReadError(NetworkError):
 
 class WriteError(NetworkError):
     pass
+
+
+class SSLError(ssl.SSLError, ConnectError):
+    pass