Intelligent reflecting surfaces (IRSs) con-stitute passive devices, which are capable of adjust-ing the phase shifts of their reflected signals, and hence they are suitable for passive beamforming. In this paper, we conceive their design with the ac-tive beamforming action of multiple-input multiple-output (MIMO) systems used at the access points (APs) for improving the beamforming gain, where both the APs and users are equipped with multiple an-tennas. Firstly, we decouple the optimization prob-lem and design the active beamforming for a given IRS configuration. Then we transform the optimiza-tion problem of the IRS-based passive beamforming design into a tractable non-convex quadratically con-strained quadratic program (QCQP). For solving the transformed problem, we give an approximate solution based on the technique of widely used semidefinite relaxation (SDR). We also propose a low-complexity iterative solution. We further prove that it can con-verge to a locally optimal value. Finally, considering the practical scenario of discrete phase shifts at the IRS, we give the quantization design for IRS elements on basis of the two solutions. Our simulation results demonstrate the superiority of the proposed solutions over the relevant benchmarks.