Aiming at the uplink multiuser Multiple Input Multiple Output(MIMO) system,a new algorithm is proposed with the maximum Signal-to-Interference Noise Ratio(SINR) guideline for Multiple Access Interference(MAI) suppression. The algorithm makes full use of the Channel State Information(CSI) to design a filter to suppress multiple access interference caused by multiple access interference and noise. In comparison with Block Diagonalization(BD) algorithm,the proposed algorithm takes the influence of noise into account,and its performance is greatly improved. The algorithm under imperfect channel scenarios is modified, and it exhibits good performance in the simulation results.