This paper proposes a new model predictive control (MPC) method for linear parameter varying systems with bounded parameter variation subject to input constraints. The method adopts closed-loop prediction and constructs ellipsoidal sets to predict the future states with reasonable computational effort. Then the information on the parameter variation rate is exploited to improve the accuracy of the prediction. Furthermore, a relaxed terminal condition, which guarantees the stability for infinite horizon, is introduced to enlarge the stabilizable region. It is shown that the feasibility of the MPC problem at the initial step ensures the stability of the closed-loop system. Finally, a simulation result illustrates the effectiveness of the proposed method.