Among the existing harmonic current suppression methods, it is difficult and complicated to suppress any nth harmonic current accurately for multi-phase permanent magnet synchronous motors (PMSMs). To solve this problem, this paper takes a five-phase dual-rotor PMSM fed with a current source inverter (CSI) as an example, and proposes an nth harmonic current suppression method based on the impulse current PWM algorithm. Firstly, the analysis is conducted and presented for the nth harmonic current in the mth harmonic space. Then, based on the Sliding Discrete Fourier Transformation (SDFT), a low-pass filter (LPF) named SDFT-LPF is designed. Additionally, the impulse current PWM technique for the five-phase CSI is realized. In this paper, the experiments have confirmed that the SDFT-LPF has good filter performance. Compared with the SVPWM, the impulse current PWM technique has the same DC-link current utilization rate, but it is easier to implement. Moreover, the proposed harmonic current control method can accurately control any nth harmonic current without changing the PWM technique, which has significantly reduced the complexity of the harmonic current control. Additionally, the proposed scheme is easy to implement and can be directly extended to the multiple harmonic current’s control.