This paper presents a power-rate attracting law based design method of discrete-time multi-periodic repetitive controllers for the problem of general multi-periodic disturbances rejection. The multi-periodic disturbance is a superposition of multiple periodic disturbances with known periods. According to the symmetry of periodic disturbance, a measure of disturbance rejection is embedded in the power-rate attracting law, thus developing the sub-repetitive controller, and the parallel-mode multi-periodic repetitive controller is designed. The multi-periodic disturbance is rejected completely, and slowtime-varying aperiodic disturbance is suppressed effectively. In order to characterize the tracking performance, we derive the expressions for the range of the power absolute attractive layer and the steady-state error band. Simulation results show the effectiveness of the presented control method.