In this paper, we study a filter design which maximizes the weighted sum rate (WSR) in multi-user multi-relay systems equipped with multiple antennas at each node and account for the direct links between the base station and the mobile users. Since this problem is generally non-convex, it is quite complicated to analytically find a solution. Hence, we transform the WSR maximization problem to an equivalent weighted sum mean-squared-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 which guarantees a local optimum solution. Through simulations, we confirm the effectiveness of our proposed scheme.