In this paper, a discrete-time preview-repetitive control method using an ARMAX model is presented and experimental results are reported. At each sampling time, a control input is modified so as to minimize the cost function on predicted future tracking errors for a prediction horizon. The sufficient conditions for the stability of the control system are derived. The preview-repetitive control system includes a phase lead compensator and the amount of phase lead is proportional to the length of the prediction horizon. This method was applied to a position control of a DC servomotor. A simple model was used for predictions. However, the stability conditions were satisfied by extending the prediction horizon. Experimental results showed that errors were reduced very quickly and did not increase after the convergence. In the 1000th period, a one-pulse error occurred one time only through the period. A stable high-precision tracking property was achieved.