diff --git a/doc/source/whatsnew/v0.25.0.rst b/doc/source/whatsnew/v0.25.0.rst
index c441244b4415d..b38bc92c6bd86 100644
--- a/doc/source/whatsnew/v0.25.0.rst
+++ b/doc/source/whatsnew/v0.25.0.rst
@@ -273,7 +273,7 @@ Datetimelike
 Timedelta
 ^^^^^^^^^
 
--
+- Bug with comparisons between :class:`Timedelta` and ``NaT`` raising ``TypeError`` (:issue:`26039`)
 -
 -
 
diff --git a/pandas/_libs/tslibs/timedeltas.pyx b/pandas/_libs/tslibs/timedeltas.pyx
index 8b71d64db26c6..c1edb664a79a7 100644
--- a/pandas/_libs/tslibs/timedeltas.pyx
+++ b/pandas/_libs/tslibs/timedeltas.pyx
@@ -779,11 +779,14 @@ cdef class _Timedelta(timedelta):
                     return PyObject_RichCompare(np.array([self]), other, op)
                 return PyObject_RichCompare(other, self, reverse_ops[op])
             else:
-                if op == Py_EQ:
+                if other is NaT:
+                    return PyObject_RichCompare(other, self, reverse_ops[op])
+                elif op == Py_EQ:
                     return False
                 elif op == Py_NE:
                     return True
-                raise TypeError('Cannot compare type {cls} with type {other}'
+                raise TypeError('Cannot compare type {cls} with '
+                                'type {other}'
                                 .format(cls=type(self).__name__,
                                         other=type(other).__name__))
 
diff --git a/pandas/conftest.py b/pandas/conftest.py
index 1cb518f426299..8f885c3aae928 100644
--- a/pandas/conftest.py
+++ b/pandas/conftest.py
@@ -218,6 +218,19 @@ def all_compare_operators(request):
     return request.param
 
 
+@pytest.fixture(params=['__le__', '__lt__', '__ge__', '__gt__'])
+def compare_operators_no_eq_ne(request):
+    """
+    Fixture for dunder names for compare operations except == and !=
+
+    * >=
+    * >
+    * <
+    * <=
+    """
+    return request.param
+
+
 @pytest.fixture(params=[None, 'gzip', 'bz2', 'zip', 'xz'])
 def compression(request):
     """
diff --git a/pandas/tests/scalar/test_nat.py b/pandas/tests/scalar/test_nat.py
index 43747ea8621d9..0ae4d107d85bd 100644
--- a/pandas/tests/scalar/test_nat.py
+++ b/pandas/tests/scalar/test_nat.py
@@ -348,3 +348,12 @@ def test_to_numpy_alias():
     result = NaT.to_numpy()
 
     assert isna(expected) and isna(result)
+
+
+@pytest.mark.parametrize("other", [
+    Timedelta(0), Timestamp(0)
+])
+def test_nat_comparisons(compare_operators_no_eq_ne, other):
+    # GH 26039
+    assert getattr(NaT, compare_operators_no_eq_ne)(other) is False
+    assert getattr(other, compare_operators_no_eq_ne)(NaT) is False