Gaussian mixture models (GMMs) have proven extremely successful for text-independent speaker recognition. The standard training method for GMMmodels is to use MAP adaptation of the means of the mixture components based on speech from a target speaker. Recent methods in compensation for speaker and channel variability have proposed the idea of stacking the means of the GMM model to form a GMM mean supervector. We examine the idea of using the GMM supervector in a support vector machine (SVM) classifier. We propose two new SVM kernels based on distance metrics between GMM models. We show that these SVM kernels produce excellent classification accuracy in a NIST speaker recognition evaluation task.