diff --git a/litellm/utils.py b/litellm/utils.py
index 584ab8805a0..7576e3bb83d 100644
--- a/litellm/utils.py
+++ b/litellm/utils.py
@@ -2780,7 +2780,7 @@ def register_model(model_cost: Union[str, dict]):  # noqa: PLR0915
         elif value.get("litellm_provider") == "openrouter":
             split_string = key.split("/", 1)
             if key not in litellm.openrouter_models:
-                litellm.openrouter_models.add(split_string[1])
+                litellm.openrouter_models.add(split_string[-1])
         elif value.get("litellm_provider") == "vercel_ai_gateway":
             if key not in litellm.vercel_ai_gateway_models:
                 litellm.vercel_ai_gateway_models.add(key)
diff --git a/tests/test_litellm/test_utils.py b/tests/test_litellm/test_utils.py
index f6c24d19df5..6d99d64f7b2 100644
--- a/tests/test_litellm/test_utils.py
+++ b/tests/test_litellm/test_utils.py
@@ -2300,6 +2300,64 @@ def test_register_model_with_scientific_notation():
     assert registered_model["mode"] == "chat"
 
 
+def test_register_model_openrouter_without_slash():
+    """
+    Test that register_model handles openrouter models without '/' in the name.
+
+    Fixes https://github.com/BerriAI/litellm/issues/18936
+
+    Previously, the code did `split_string[1]` which would fail with IndexError
+    when the model name didn't contain '/'. Now it uses `split_string[-1]` which
+    always works.
+    """
+    # Clear any existing entries
+    litellm.openrouter_models.discard("my-custom-alias")
+    litellm.openrouter_models.discard("gpt-4")
+    litellm.openrouter_models.discard("openai/gpt-4")
+
+    # Test 1: Model name without '/' (this was the bug - would raise IndexError)
+    litellm.register_model(
+        {
+            "my-custom-alias": {
+                "max_tokens": 8192,
+                "input_cost_per_token": 0.00001,
+                "output_cost_per_token": 0.00002,
+                "litellm_provider": "openrouter",
+                "mode": "chat",
+            },
+        }
+    )
+    assert "my-custom-alias" in litellm.openrouter_models
+
+    # Test 2: Model name with single '/' (openrouter/model format)
+    litellm.register_model(
+        {
+            "openrouter/gpt-4": {
+                "max_tokens": 8192,
+                "input_cost_per_token": 0.00001,
+                "output_cost_per_token": 0.00002,
+                "litellm_provider": "openrouter",
+                "mode": "chat",
+            },
+        }
+    )
+    assert "gpt-4" in litellm.openrouter_models
+
+    # Test 3: Model name with double '/' (openrouter/provider/model format)
+    litellm.register_model(
+        {
+            "openrouter/openai/gpt-4-turbo": {
+                "max_tokens": 8192,
+                "input_cost_per_token": 0.00001,
+                "output_cost_per_token": 0.00002,
+                "litellm_provider": "openrouter",
+                "mode": "chat",
+            },
+        }
+    )
+    assert "openai/gpt-4-turbo" in litellm.openrouter_models
+
+
 def test_reasoning_content_preserved_in_text_completion_wrapper():
     """Ensure reasoning_content is copied from delta to text_choices."""
     chunk = ModelResponseStream(