Abstract: ‍ ‍Intelligent reflective surface （IRS） is considered as one of the promising technologies for wireless communication networks. However， due to the non-convex constant modulus constraint of IRS passive beam forming optimization， existing researches in IRS-assisted multiple input multiple output （MIMO） systems only got suboptimal solutions with high complexity. The paper considered a single-user IRS-assisted communication millimeter-wave MIMO system. In order to maximize the spectrum efficiency， the active beamforming matrix at the AP （access point） side and the passive beamforming matrix at the IRS side were optimized. Firstly， the active and passive beamforming matrices were decoupled to obtain the optimal active beamforming solution for AP. The IRS passive beamforming design problem was derived as a non-convex quadratically constrained quadratic programming （QCQP） problem. The low-complexity successive closed form （SCF） algorithm was used to solve the IRS passive beamforming matrix. In order to measure the performance of the SCF algorithm， the existing optimal branch and bound （BnB） algorithm was analyzed and compared. The simulation results verify that the SCF algorithm can achieve higher spectral efficiency performance with lower complexity when the IRS phase shift is continuous and discrete.