Recently, reconfigurable intelligent surface (RIS) has arisen as an excellent technology for assisting wireless communications. In order to handle the intractable non-convex problem for jointly optimizing beamforming and PSs in multiple-input multipleoutput (MIMO) transmission, we propose a novel alternating direction (AD) method by maximizing the achievable rate (AR) at the receiver. Specifically, the initial problem is divided into the following two processes: i) optimizing the beamforming vector with fixed PSs, ii) determining a specific PS based on a closedform solution when the other PSs and beamforming are fixed. Simulation results corroborate that the proposed AD method provides robust attainable performance with reduced computational complexity compared to its traditional counterparts.