In this paper, a robust model predictive control (MPC) technique is introduced to control MIMO linear parameter-varying (LPV) systems subject to input-output constraints. The LPV system is represented in input-output form, which is a common form obtained through LPV system identification. The method guarantees asymptotic stability of the closed-loop system and provides integral action for a given piecewise constant reference trajectory based on past measurements of the inputs and outputs. The technique offers computationally more efficient and less conservative design approach compared to previous works. A simulation example is given to demonstrate the effectiveness of the proposed technique.