To improve the performance of six-phase permanent magnet synchronous generator (PMSG) after the occurrence of single-phase open-circuit fault, a stationary coordinate transform matrix suit to fault-tolerant control strategy is built and voltage and torque equations in rotating coordinate system, in which the affect of the third harmonics is considered, are established. In allusion to the situation that the voltage model cannot be completely decoupled by once of rotating coordinate transformation, it is proposed to apply rotating coordinate transformation twice to the d-q sub-space to achieve completely decoupled voltage components on d-q axis. Based on the invariance principle of magnetic potential, a closed-loop control strategy of stator current magnitude minimum (SCMM) is given, and to suppress the affects of the third harmonic magnetic flux linkage and the third harmonic inductance, the compensation quantities for the third harmonic voltages on d-q axis are derived. The validity of suppressing the affect of the third harmonic by the proposed compensation and control strategy is verified by results of simulation and experiments, and the performance of six-phase PMSG after the occurrence of single-phase open-circuit fault under the control strategy of SCMM is evidently improved.