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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 [Formula: see text] space) of SVM are arbitrarily distributed among [Formula: see text] 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 [Formula: see text]-approximation algorithm to reach this lower bound, where [Formula: see text] is a user specified small constant. For distributed SVM with outliers, we present a [Formula: see text]-approximation algorithm to explicitly remove the influence of outliers. Our algorithm is based on a deterministic distributed top [Formula: see text] selection algorithm with communication complexity of [Formula: see text] in the coordinator model.