There existed large current harmonics when the variable frequency air conditioner ran in the low frequency. When using the common repetitive control (RC), since the ratio of the sampling frequency to the fundamental frequency of current harmonics may be not an integer, there was deviation between the internal mode of repetitive control and the fundamental frequency of the current harmonics, and thus the suppression effects of the repetitive controller would be degraded drastically. Aiming at this problem, a fractionalorder RC (FORC) strategy at fixed sampling frequency was proposed. Firstly, Lagrange interpolation theory was used to approximate the fractional delay item; secondly, FIR filter was used to eliminate the error caused by low pass filter (LPF); finally, aiming at the phase lag of the FORC, phase compensation was made in all frequency bands to confirm the stability of the closed loop. The experiment results showed that the proposed strategy could effectively suppress the current harmonics of the variable frequency air conditioner running at the low frequency.