diff --git a/replicate/client.py b/replicate/client.py
index b267e1c1..2441a4c7 100644
--- a/replicate/client.py
+++ b/replicate/client.py
@@ -329,9 +329,8 @@ def _build_httpx_client(
     timeout: Optional[httpx.Timeout] = None,
     **kwargs,
 ) -> Union[httpx.Client, httpx.AsyncClient]:
-    headers = {
-        "User-Agent": f"replicate-python/{__version__}",
-    }
+    headers = kwargs.pop("headers", {})
+    headers["User-Agent"] = f"replicate-python/{__version__}"
 
     if (
         api_token := api_token or os.environ.get("REPLICATE_API_TOKEN")
diff --git a/tests/test_client.py b/tests/test_client.py
index 163b185e..ee345203 100644
--- a/tests/test_client.py
+++ b/tests/test_client.py
@@ -85,3 +85,27 @@ async def test_server_error_handling():
             client._request("GET", "/")
         assert "status: 500" in str(exc_info.value)
         assert "detail: Server error occurred" in str(exc_info.value)
+
+
+def test_custom_headers_are_applied():
+    import replicate
+    from replicate.exceptions import ReplicateError
+
+    custom_headers = {"Custom-Header": "CustomValue"}
+
+    def mock_send(request: httpx.Request, **kwargs) -> httpx.Response:
+        assert "Custom-Header" in request.headers
+        assert request.headers["Custom-Header"] == "CustomValue"
+
+        return httpx.Response(401, json={})
+
+    client = replicate.Client(
+        api_token="dummy_token",
+        headers=custom_headers,
+        transport=httpx.MockTransport(mock_send),
+    )
+
+    try:
+        client.accounts.current()
+    except ReplicateError:
+        pass