A complex-coefficient repetitive controller (CRC) is proposed to improve the tracking performance of the system for periodic signals. The CRC includes a complex-coefficient filter, a time-delay positive feedback loop, and an integral controller. Unlike the widely used low-pass filters, the complex-coefficient filter can reduce the phase lag of the control signal at the harmonic frequency of the periodic signal without changing the cutoff frequency. Thus, the complex-coefficient repetitive-control system can improve the tracking performance of the system without amplifying the measurement noise of the system. Simulations for the speed control system illustrate the effectiveness and superiority of the proposed method.