In the last decade, Support vector machine (SVM) has been deeply investigated and it is often used in Hilbert space by the measure of Euclidean distance. In this paper, we present the SVM with mahalanobis distance, and the details of how to compute the mahalanobis distance in the input and the feature space are described. Finally, we apply it to the image classification and compare the results of them. By this, we obtain a sound conclusion.