diff --git a/pytests/test_dag_cbor.py b/pytests/test_dag_cbor.py
index d589d76..d0f7ee5 100644
--- a/pytests/test_dag_cbor.py
+++ b/pytests/test_dag_cbor.py
@@ -179,3 +179,51 @@ def test_dab_cbor_encode_map_int_key() -> None:
         libipld.encode_dag_cbor(obj)
 
     assert 'Map keys must be strings' in str(exc_info.value)
+
+
+def test_dag_cbor_decode_nan_f64_error() -> None:
+    # fb7ff8000000000000 - IEEE 754 double precision NaN
+    with pytest.raises(ValueError) as exc_info:
+        libipld.decode_dag_cbor(bytes.fromhex('fb7ff8000000000000'))
+
+    assert 'number out of range for f64' in str(exc_info.value).lower()
+
+
+def test_dag_cbor_decode_positive_infinity_f64_error() -> None:
+    # fb7ff0000000000000 - IEEE 754 double precision positive infinity
+    with pytest.raises(ValueError) as exc_info:
+        libipld.decode_dag_cbor(bytes.fromhex('fb7ff0000000000000'))
+
+    assert 'number out of range for f64' in str(exc_info.value).lower()
+
+
+def test_dag_cbor_decode_negative_infinity_f64_error() -> None:
+    # fbfff0000000000000 - IEEE 754 double precision negative infinity
+    with pytest.raises(ValueError) as exc_info:
+        libipld.decode_dag_cbor(bytes.fromhex('fbfff0000000000000'))
+
+    assert 'number out of range for f64' in str(exc_info.value).lower()
+
+
+def test_dag_cbor_decode_nan_f32_error() -> None:
+    # fa7fc00000 - IEEE 754 single precision NaN
+    with pytest.raises(ValueError) as exc_info:
+        libipld.decode_dag_cbor(bytes.fromhex('fa7fc00000'))
+
+    assert 'number out of range for f32' in str(exc_info.value).lower()
+
+
+def test_dag_cbor_decode_positive_infinity_f32_error() -> None:
+    # fa7f800000 - IEEE 754 single precision positive infinity
+    with pytest.raises(ValueError) as exc_info:
+        libipld.decode_dag_cbor(bytes.fromhex('fa7f800000'))
+
+    assert 'number out of range for f32' in str(exc_info.value).lower()
+
+
+def test_dag_cbor_decode_negative_infinity_f32_error() -> None:
+    # faff800000 - IEEE 754 single precision negative infinity
+    with pytest.raises(ValueError) as exc_info:
+        libipld.decode_dag_cbor(bytes.fromhex('faff800000'))
+
+    assert 'number out of range for f32' in str(exc_info.value).lower()
diff --git a/src/lib.rs b/src/lib.rs
index 5b4c383..140dae6 100644
--- a/src/lib.rs
+++ b/src/lib.rs
@@ -199,8 +199,20 @@ fn decode_dag_cbor_to_pyobject<R: Read + Seek>(
             cbor::FALSE => false.into_pyobject(py)?.into_any().unbind(),
             cbor::TRUE => true.into_pyobject(py)?.into_any().unbind(),
             cbor::NULL => py.None(),
-            cbor::F32 => decode::read_f32(r)?.into_pyobject(py)?.into(),
-            cbor::F64 => decode::read_f64(r)?.into_pyobject(py)?.into(),
+            cbor::F32 => {
+                let value = decode::read_f32(r)?;
+                if !value.is_finite() {
+                    return Err(anyhow!("Number out of range for f32 (NaNs are forbidden)".to_string()));
+                }
+                value.into_pyobject(py)?.into()
+            },
+            cbor::F64 => {
+                let value = decode::read_f64(r)?;
+                if !value.is_finite() {
+                    return Err(anyhow!("Number out of range for f64 (NaNs are forbidden)".to_string()));
+                }
+                value.into_pyobject(py)?.into()
+            },
             _ => return Err(anyhow!("Unsupported major type".to_string())),
         },
     })