diff --git a/fastapi/params.py b/fastapi/params.py
index 860146531..7c35a571b 100644
--- a/fastapi/params.py
+++ b/fastapi/params.py
@@ -91,7 +91,7 @@ class Param(FieldInfo):
             max_length=max_length,
             discriminator=discriminator,
             multiple_of=multiple_of,
-            allow_nan=allow_inf_nan,
+            allow_inf_nan=allow_inf_nan,
             max_digits=max_digits,
             decimal_places=decimal_places,
             **extra,
diff --git a/test_param_allow_inf_nan.py b/test_param_allow_inf_nan.py
new file mode 100644
index 000000000..4488eeaea
--- /dev/null
+++ b/test_param_allow_inf_nan.py
@@ -0,0 +1,58 @@
+from typing import Optional
+
+from fastapi import FastAPI
+from fastapi.params import Query
+from fastapi.testclient import TestClient
+
+app = FastAPI()
+
+@app.get("/")
+def get(
+        x: Optional[float] = Query(default=0, allow_inf_nan=False),
+        y: Optional[float] = Query(default=0, allow_inf_nan=True),
+        z: Optional[float] = Query(default=0)) -> str:  # type: ignore
+    return 'OK'
+
+
+client = TestClient(app)
+
+
+def test_allow_inf_nan_false():
+    response = client.get('/?x=inf')
+    assert response.status_code == 422, response.text
+    
+    response = client.get('/?x=-inf')
+    assert response.status_code == 422, response.text
+    
+    response = client.get('/?x=nan')
+    assert response.status_code == 422, response.text
+
+    response = client.get('/?x=0')
+    assert response.status_code == 200, response.text
+
+def test_allow_inf_nan_true():
+    response = client.get('/?y=inf')
+    assert response.status_code == 200, response.text
+    
+    response = client.get('/?y=-inf')
+    assert response.status_code == 200, response.text
+    
+    response = client.get('/?y=nan')
+    assert response.status_code == 200, response.text
+
+    response = client.get('/?y=0')
+    assert response.status_code == 200, response.text
+
+def test_allow_inf_nan_not_specified():
+    response = client.get('/?z=inf')
+    assert response.status_code == 200, response.text
+    
+    response = client.get('/?z=-inf')
+    assert response.status_code == 200, response.text
+    
+    response = client.get('/?z=nan')
+    assert response.status_code == 200, response.text
+
+    response = client.get('/?z=0')
+    assert response.status_code == 200, response.text
+