Abstract This paper deals with the control of a catalytic reverse flow reactor (RFR) used for methane combustion. The periodic flow reversals effected on the system makes it both continuous and discrete in nature (i.e., a hybrid system). Control of this system is challenging due to the unsteady state behavior of the process along with its mixed discrete and continuous behavior. Although model predictive control (MPC) is proven to be a powerful technique for several processes it becomes less effective in systems such as the RFR where the model prediction errors and the effect of disturbances on the plant output repeat from time to time. In such cases, control can be improved if the repetitive error pattern is exploited. A novel repetitive model predictive control (RMPC) strategy, that combines the basic concepts of iterative learning control (ILC) and repetitive control (RC) along with the concepts of MPC, is proposed for such systems. In the proposed strategy, the state variables of the model are reset periodically along with predictive control action such that the process follows the reference trajectory as closely as possible. The results obtained prove that the RMPC approach provides an excellent performance for the control of the RFR.