diff --git a/GPy/kern/__init__.py b/GPy/kern/__init__.py
index 164b66b7..d8239910 100644
--- a/GPy/kern/__init__.py
+++ b/GPy/kern/__init__.py
@@ -32,7 +32,7 @@ from .src.trunclinear import TruncLinear,TruncLinear_inf
 from .src.splitKern import SplitKern,DEtime
 from .src.splitKern import DEtime as DiffGenomeKern
 from .src.spline import Spline
-from .src.basis_funcs import LogisticBasisFuncKernel, LinearSlopeBasisFuncKernel, BasisFuncKernel, ChangePointBasisFuncKernel, DomainKernel
+from .src.basis_funcs import LogisticBasisFuncKernel, LinearSlopeBasisFuncKernel, BasisFuncKernel, ChangePointBasisFuncKernel, DomainKernel, PolynomialBasisFuncKernel
 from .src.grid_kerns import GridRBF
 
 from .src.sde_matern import sde_Matern32
diff --git a/GPy/kern/src/basis_funcs.py b/GPy/kern/src/basis_funcs.py
index 5d589aa6..569a12f1 100644
--- a/GPy/kern/src/basis_funcs.py
+++ b/GPy/kern/src/basis_funcs.py
@@ -102,6 +102,26 @@ class BasisFuncKernel(Kern):
                 phi2 = phi2[:, None]
             return phi1.dot(phi2.T)
 
+class PolynomialBasisFuncKernel(BasisFuncKernel):
+    def __init__(self, input_dim, degree, variance=1., active_dims=None, ARD=True, name='polynomial_basis'):
+        """
+        A linear segment transformation. The segments start at start, \
+        are then linear to stop and constant again. The segments are
+        normalized, so that they have exactly as much mass above
+        as below the origin.
+
+        Start and stop can be tuples or lists of starts and stops.
+        Behaviour of start stop is as np.where(X<start) would do.
+        """
+        self.degree = degree
+        super(PolynomialBasisFuncKernel, self).__init__(input_dim, variance, active_dims, ARD, name)
+
+    @Cache_this(limit=3, ignore_args=())
+    def _phi(self, X):
+        phi = np.empty((X.shape[0], self.degree+1))
+        for i in range(self.degree+1):
+            phi[:, [i]] = X**i
+        return phi
 
 class LinearSlopeBasisFuncKernel(BasisFuncKernel):
     def __init__(self, input_dim, start, stop, variance=1., active_dims=None, ARD=False, name='linear_segment'):
diff --git a/GPy/testing/kernel_tests.py b/GPy/testing/kernel_tests.py
index 5babeb41..c2725c8e 100644
--- a/GPy/testing/kernel_tests.py
+++ b/GPy/testing/kernel_tests.py
@@ -495,6 +495,13 @@ class KernelGradientTestsContinuous(unittest.TestCase):
         k = GPy.kern.Add(ks)
         self.assertTrue(check_kernel_gradient_functions(k, X=self.X, X2=self.X2, verbose=verbose))
 
+    def test_basis_func_poly(self):
+        ks = []
+        for i in range(self.X.shape[1]):
+            ks.append(GPy.kern.PolynomialBasisFuncKernel(1, 5, ARD=i%2==0, active_dims=[i]))
+        k = GPy.kern.Add(ks)
+        self.assertTrue(check_kernel_gradient_functions(k, X=self.X, X2=self.X2, verbose=verbose))
+
     def test_basis_func_domain(self):
         start_stop = np.random.uniform(self.X.min(0), self.X.max(0), (4, self.X.shape[1])).T
         start_stop.sort(axis=1)