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In this paper, we study a filter design that maximizes the weighted sum rate (WSR) in multiuser multirelay systems equipped with multiple antennas at each node. Since this problem is generally nonconvex, it is quite complicated to analytically find a solution. Hence, we transform the WSR maximization problem to an equivalent weighted sum mean-square-error (WSMSE) minimization problem, which is more amenable. Then, we identify the filters at the base station and the relays for minimizing the WSMSE with a proper weight and propose an alternating computation algorithm that guarantees a local optimum solution. Through simulations, we confirm the effectiveness of our proposed scheme.