This paper presents a design method of a discrete-time sliding mode multi-periodic repetitive controller for the multi-periodic disturbance suppress problem of discrete-time systems. A novel reaching law is designed using the nonlinear power function, periodic difference equivalent disturbance in weighted form is embedded in the reaching law to form a discrete reaching law with disturbance compensation, and thus developing the discrete-time sliding mode multi-period repetitive controller. In order to adjust the control parameters and characterize the convergent performance of the closed-loop system, we derive the expression of the quasi-sliding mode domain. The developed control method not only achieves the rejection of multi-periodic disturbances, but also can obtain the smaller quasi-sliding mode boundary layer. Simulation results validate the effectiveness of the presented control method.