Non-ideal factors can cause steady-state speed ripples for Permanent Magnet Synchronous Motor (PMSM). In this paper current measurement error is mainly analyzed since it can cause multiple (not only 1st- or 2nd-order as analyzed in the existing literature) harmonics when considering its influence on electrical angle. In order to suppress the ripples, a robust plug-in repetitive controller with phase compensation is designed in the outer speed loop of PMSM cascade PI control system. Compared with the repetitive controller added in the current loop, there are two technical challenges: more stringent requirement of high-frequency disturbance suppression and more complex phase compensation design. Hence, a third-order Butterworth filter with phase correction is proposed which can ensure the system’s ability to resist low-frequency periodic disturbances and the high-frequency stability of the system. A hybrid phase correction method combining lead, lag and linear correction is designed which can ensure the stability and the fast convergence of the system at low frequencies. The designed repetitive controller is robust to PMSM parameters variation within a normal range. The experimental results prove that the proposed control strategy can effectively suppress motor speed fluctuation with good steady-state and transient performance.