diff --git a/GPy/kern/__init__.py b/GPy/kern/__init__.py
index 3c3de65c..7f44b6a9 100644
--- a/GPy/kern/__init__.py
+++ b/GPy/kern/__init__.py
@@ -10,7 +10,7 @@ from .src.add import Add
 from .src.prod import Prod
 from .src.rbf import RBF
 from .src.linear import Linear, LinearFull
-from .src.static import Bias, White, Fixed, WhiteHeteroscedastic
+from .src.static import Bias, White, Fixed, WhiteHeteroscedastic, Precomputed
 from .src.brownian import Brownian
 from .src.stationary import Exponential, OU, Matern32, Matern52, ExpQuad, RatQuad, Cosine
 from .src.mlp import MLP
diff --git a/GPy/kern/src/static.py b/GPy/kern/src/static.py
index 18f7605f..c2f6b129 100644
--- a/GPy/kern/src/static.py
+++ b/GPy/kern/src/static.py
@@ -192,3 +192,53 @@ class Fixed(Static):
     def update_gradients_expectations(self, dL_dpsi0, dL_dpsi1, dL_dpsi2, Z, variational_posterior):
         self.variance.gradient = dL_dpsi0.sum()
 
+class Precomputed(Fixed):
+    def __init__(self, input_dim, covariance_matrix, variance=1., active_dims=None, name='precomputed'):
+        """
+        Class for precomputed kernels, indexed by X
+        
+        Usage example:
+        
+        import numpy as np
+        from GPy.models import GPClassification
+        from GPy.kern import Precomputed
+        from sklearn.cross_validation import LeaveOneOut
+        
+        n = 10
+        d = 100
+        X = np.arange(n).reshape((n,1))         # column vector of indices
+        y = 2*np.random.binomial(1,0.5,(n,1))-1
+        X0 = np.random.randn(n,d)
+        k = np.dot(X0,X0.T)
+        kern = Precomputed(1,k)                 # k is a n x n covariance matrix
+        
+        cv = LeaveOneOut(n)
+        ypred = y.copy()
+        for train, test in cv:
+            m = GPClassification(X[train], y[train], kernel=kern)
+            m.optimize()
+            ypred[test] = 2*(m.predict(X[test])[0]>0.5)-1
+        
+        :param input_dim: the number of input dimensions
+        :type input_dim: int
+        :param variance: the variance of the kernel
+        :type variance: float
+        """
+        super(Precomputed, self).__init__(input_dim, covariance_matrix, variance, active_dims, name)
+    def K(self, X, X2=None):
+        if X2 is None:
+            return self.variance * self.fixed_K[X[:,0].astype('int')][:,X[:,0].astype('int')]
+        else:
+            return self.variance * self.fixed_K[X[:,0].astype('int')][:,X2[:,0].astype('int')]
+
+    def Kdiag(self, X):
+        return self.variance * self.fixed_K[X[:,0].astype('int')][:,X[:,0].astype('int')].diagonal()
+
+    def update_gradients_full(self, dL_dK, X, X2=None):
+        if X2 is None:
+            self.variance.gradient = np.einsum('ij,ij', dL_dK, self.fixed_K[X[:,0].astype('int')][:,X[:,0].astype('int')])
+        else:
+            self.variance.gradient = np.einsum('ij,ij', dL_dK, self.fixed_K[X[:,0].astype('int')][:,X2[:,0].astype('int')])
+
+    def update_gradients_diag(self, dL_dKdiag, X):
+        self.variance.gradient = np.einsum('i,ii', dL_dKdiag, self.fixed_K[X[:,0].astype('int')][:,X[:,0].astype('int')])
\ No newline at end of file
diff --git a/GPy/testing/kernel_tests.py b/GPy/testing/kernel_tests.py
index 6b620406..cab0c3e9 100644
--- a/GPy/testing/kernel_tests.py
+++ b/GPy/testing/kernel_tests.py
@@ -339,6 +339,15 @@ class KernelGradientTestsContinuous(unittest.TestCase):
         k = GPy.kern.StdPeriodic(self.D)
         k.randomize()
         self.assertTrue(check_kernel_gradient_functions(k, X=self.X, X2=self.X2, verbose=verbose))
+        
+    def test_Precomputed(self):
+        Xall = np.concatenate([self.X, self.X2])
+        cov = np.dot(Xall, Xall.T)
+        X = np.arange(self.N).reshape(1,self.N)
+        X2 = np.arange(self.N,2*self.N+10).reshape(1,self.N+10)
+        k = GPy.kern.Precomputed(1, cov)
+        k.randomize()
+        self.assertTrue(check_kernel_gradient_functions(k, X=X, X2=X2, verbose=verbose))
 
 class KernelTestsMiscellaneous(unittest.TestCase):
     def setUp(self):