This paper investigates an intelligent reflecting surface (IRS) assisted multi-input multi-output (MIMO) simultaneous wireless information and power transfer (SWIPT) system with multiple power splitting receivers (PSRs). We aim at maximizing the weighted sum-rate (WSR) of the system through jointly designing the PS ratio of each PSR, the active transmit beamforming (ATB) of the access point (AP) and the passive reflective beamforming (PRB) of the IRS, while the constraints on the AP, PSRs and IRS are satisfied. However, since the variables are intricately coupled and the constraints are conflicting, the formulated problem is non-convex. We propose a framework to jointly design the AP, the PSRs and the IRS. Particularly, first we transform this problem into an equivalently form based on fractional programming methods. Then, we decompose the transformed problem into several subproblems, and more important, we exploit the successive convex approximation method to recast the non-convex constraints, so as to transform the subproblems as convex form and then solve them alternately. Simulation results indicate that the proposed algorithm achieves a substantial improvement performance gain over baseline schemes.