A discrete-time repetitive control method is proposed for systems with periodic reference signals. A measure of disturbance-rejection is embedded in the attracting law by using the dead-zone function to form the ideal error dynamics, by which the discrete-time repetitive controller is derived. For the convenience in adjusting the controller parameters and describing the error dynamics of the closed-loop system, the expressions for the range of the steady-state error, the boundary of the monotonically decreasing region and the absolute attractive layer are derived. The developed repetitive controller is not only effective in rejection of the periodic disturbances, but also applicable to position control with constant regulation problems. Both numerical simulation and experiment results on a servomechanism are given to verify the feasibility and effectiveness of the proposed control method.