In this paper, we consider the distributed version of Support Vector Machine (SVM) under the coordinator model, where all input data (i.e., points in ℝd space) of SVM are arbitrarily distributed among k nodes in some network with a coordinator which can communicate with all nodes. We investigate two variants of this problem, with and without outliers. For distributed SVM without outliers, we prove a lower bound on the communication complexity and give a distributed (1 - ε)-approximation algorithm to reach this lower bound, where ε is a user specified small constant. For distributed SVM with outliers, we present a (1 - ε)-approximation algorithm to explicitly remove the influence of outliers. Our algorithm is based on a deterministic distributed top t selection algorithm with communication complexity of O(k log (t)) in the coordinator model. Experimental results on benchmark datasets confirm the theoretical guarantees of our algorithms.