In many applications, data appear with a huge number of instances as well as features. Linear Support Vector Machines (SVM) is one of the most popular tools to deal with such large-scale sparse data. This paper presents a novel dual coordinate descent method for linear SVM with L1- and L2-loss functions. The proposed method is simple and reaches an epsilon-accurate solution in O(log (1/epsilon)) iterations. Experiments indicate that our method is much faster than state of the art solvers such as Pegasos, Tron, svmperf, and a recent primal coordinate descent implementation.