This paper presents a novel reduced-complexity channel estimator for Coordinated Multi-point (CoMP) multi-user systems. The proposed scheme is based on Space Alternating Generalized-EM (SAGE) algorithm combining with the Least Square (LS) criterion. Aiming at the problem that the conventional joint multi-user LS estimator introduces the complex inversion of large size matrix when using non-orthogonal pilots, the proposed estimator avoids the inverse operation by transforming the joint multi-user estimation into a series of single-user estimating process in an iterative way. Simulation results verify that the proposed algorithm obtain huge complexity reduction, while achieving the optimal performance of joint LS channel estimation for the CoMP systems.