diff --git a/changelog/7198.internal.rst b/changelog/7198.internal.rst
new file mode 100644
index 0000000000..aa0f1af23e
--- /dev/null
+++ b/changelog/7198.internal.rst
@@ -0,0 +1,2 @@
+:user:`01luyicheng` added unit tests for :meth:`~iris.cube.Cube.coord_dims`.
+(:issue:`4552`)
diff --git a/lib/iris/tests/unit/cube/test_Cube.py b/lib/iris/tests/unit/cube/test_Cube.py
index d91c7e81c0..560aa5e650 100644
--- a/lib/iris/tests/unit/cube/test_Cube.py
+++ b/lib/iris/tests/unit/cube/test_Cube.py
@@ -3989,3 +3989,81 @@ def test_with_data(self):
     def test_without_data(self):
         cube = Cube(data=None, shape=self.shape)
         assert cube.is_dataless()
+
+
+class Test_coord_dims:
+    """Tests for :meth:`iris.cube.Cube.coord_dims`."""
+
+    @pytest.fixture(autouse=True)
+    def _setup(self):
+        # Build a 3D cube with dimension coordinates and auxiliary
+        # coordinates spanning one and multiple dimensions.
+
+        # Set-up the cube.
+        data = np.arange(24).reshape(2, 3, 4)
+        cube = Cube(data)
+
+        # Set-up the DimCoords and add them to the cube.
+        x_coord = DimCoord(points=np.array([0, 1]), long_name="x")
+        y_coord = DimCoord(points=np.array([0, 1, 2]), long_name="y")
+        z_coord = DimCoord(points=np.array([0, 1, 2, 3]), long_name="z")
+        cube.add_dim_coord(x_coord, 0)
+        cube.add_dim_coord(y_coord, 1)
+        cube.add_dim_coord(z_coord, 2)
+
+        # Set-up the AuxCoords and add them to the cube.
+        aux_1d = AuxCoord(points=np.array([0, 1]), long_name="aux_1d")
+        aux_2d = AuxCoord(points=np.arange(6).reshape(2, 3), long_name="aux_2d")
+        cube.add_aux_coord(aux_1d, 0)
+        cube.add_aux_coord(aux_2d, (0, 1))
+
+        # Assign them all to class variables.
+        self.cube = cube
+        self.x_coord = x_coord
+        self.aux_1d = aux_1d
+        self.aux_2d = aux_2d
+
+    def test_dim_coord(self):
+        # A dimension coordinate is found by object identity.
+        assert self.cube.coord_dims(self.x_coord) == (0,)
+
+    def test_string_name(self):
+        # A coordinate may be looked up by its string name.
+        assert self.cube.coord_dims("y") == (1,)
+
+    def test_aux_coord_single_dim(self):
+        # An auxiliary coordinate spanning a single dimension.
+        assert self.cube.coord_dims(self.aux_1d) == (0,)
+
+    def test_aux_coord_multiple_dims(self):
+        # An auxiliary coordinate spanning multiple dimensions.
+        assert self.cube.coord_dims(self.aux_2d) == (0, 1)
+
+    def test_aux_factory(self):
+        # A derived coordinate provided by an aux factory.
+        # Dependencies for a hybrid-height derived coordinate ("altitude").
+        delta = AuxCoord(points=np.array([0, 1]), long_name="delta", units="m")
+        sigma = AuxCoord(points=np.array([0, 1]), long_name="sigma")
+        orography = AuxCoord(
+            np.arange(12).reshape(3, 4), units="m", long_name="orography"
+        )
+        self.cube.add_aux_coord(delta, 0)
+        self.cube.add_aux_coord(sigma, 0)
+        self.cube.add_aux_coord(orography, (1, 2))
+        factory = HybridHeightFactory(delta=delta, sigma=sigma, orography=orography)
+        self.cube.add_aux_factory(factory)
+        derived_coord = factory.make_coord(self.cube.coord_dims)
+        assert self.cube.coord_dims(derived_coord) == (0, 1, 2)
+
+    def test_equivalent_coord_not_instance(self):
+        # An equivalent coordinate (same metadata, different instance) is
+        # resolved via the fallback coordinate lookup.
+        equivalent = self.x_coord.copy()
+        assert equivalent is not self.x_coord
+        assert self.cube.coord_dims(equivalent) == (0,)
+
+    def test_no_match_raises(self):
+        # A coordinate that is not on the cube and matches nothing raises.
+        missing = DimCoord(points=np.array([0, 1]), long_name="missing")
+        with pytest.raises(CoordinateNotFoundError):
+            self.cube.coord_dims(missing)