In order to mitigate the out- of- cell and the intra- cell interferences in the cell- edge users in downlink multi- cell multi- user MIMO (Multiple- Input Multiple- Output) systems where each base station has multiple trans-mitting antennas and each mobile user has multiple receiving antennas,two interference suppression techniques respectively based on the block diagonalization and the minimum mean- squared error algorithms are proposed,and the numbers of transmitting antennas and receiving antennas affected by user number and cell number are analyzed.Simulated results indicate that the two techniques both greatly improve the spectral efficiency of cell- edge users.