Intelligent reflecting surface (IRS) is one of the key technologies in the sex generation(6G). However, for multi-user systems, the computational complexity of the system increases greatly with the increase of the number of reflective units and the number of users, and the optimal design of the system faces great challenges. In this paper, we propose a low computational complex transmission rate maximization algorithm based on multi-user reflection unit selection. According to the user′s rate requirements and channel conditions, the algorithm selects the matching reflection unit, considers the phase shift setting and the base station beamforming, and carries out joint optimization to establish a user rate maximization problem. There is a high degree of coupling between the variables in this optimization problem. Therefore, the original problem is divided into two subproblems for solving, and the approximate solution is obtained by using semidefinite relaxation. The simulation results show that the algorithm proposed in this paper can significantly reduce the computational complexity of the system while improving the downlink transmission rate. Compared to a system without IRS assistance, the transmission rate increases by about 50%; compared to a random phase IRS, the transmission rate increases by about 30%.