For the asymmetric six-phase motor fed by a two-level six-phase voltage source inverter (VSI), when the modulation index is less than 0.5774, the motor operates in the linear region, and the harmonics in the Z1 − Z2 subspace can be suppressed to zero. When the modulation index is beyond 0.5774 and less than 0.6221, the motor operates in overmodulation regions, and the harmonics in the Z1 − Z2 subspace cannot be suppressed to zero. To minimize the harmonics in the Z1 − Z2 subspace for these regions, a harmonic suppression strategy, namely, harmonic suppression overmodulation strategy (HSOS), is proposed in this paper. The lower-order harmonics of the Z1 − Z2 subspace, namely, the 5th, 7th, 17th and 19th, are considered. Compared with the traditional four-vector overmodulation strategy (TFOS), the content of the 5th harmonic is reduced by about 20%, and the total harmonic distortion (THDZ1Z2) of these four kinds of harmonics is reduced by about 21% in the proposed HSOS. Finally, the simulation and experiment are carried out to verify the effectiveness of the proposed strategy.