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In this paper we study the problem of learning a low-dimensional (sparse) distance matrix. We propose a novel metric learning model which can simultaneously conduct dimension reduction and learn a distance matrix. The sparse representation involves a mixed-norm regularization which is non-convex. We then show that it can be equivalently formulated as a convex saddle (min-max) problem. From this saddle representation, we develop an efficient smooth optimization approach for sparse metric learning although the learning model is based on a non-differential loss function. This smooth optimization approach has an optimal convergence rate of for smooth problems where is the iteration number. Finally, we run experiments to validate the effectiveness and efficiency of our sparse metric learning model on various datasets.