To eliminate the steady-state error of systems with periodic disturbance, the repetitive control (RC) is a useful approach. For practical applications, the controller is designed to both steer system output to a given set-point (or track a given reference signal) and reject periodic disturbance. The learning procedure of RC and the control action to steer system output to a set-point may influence each other and prolong the convergence time RC. In order to reduce this interaction, this paper proposes a separated design approach. A linear parameter varying (LPV) system is considered. A repetitive predictive control (RPC) and a robust model predictive control (RMPC) are separately designed, respectively, corresponding to reject the periodic disturbance and steer system output to the set-point. The convergence of the proposed RPC sub-controller is derived. The numerical examples show that the proposed design is effective. (C) 2013 Elsevier Ltd. All rights reserved.