Compared to the conventional three-phase permanent magnet (PM) machine, the multi-phase PM machine has better fault tolerant capability. In this paper, a fault-tolerant control strategy for the five-phase PM synchronous machine (FPMSM) is proposed based on current compensation by utilizing the third harmonic frame. The key of this method is to redefine the current in third harmonic subspace and realize fault-tolerant control in normal vector control system. Four compensation coefficients are utilized to describe the relationship between fundamental reference current and third harmonic reference in different open-circuit fault conditions. Values of the compensation coefficients are calculated offline and summarized, which contributes to calculate reference currents rapidly according to different fault types. In addition, in order to verify such kind of strategy, the control scheme is given and the experiment according to different fault types is implemented in this paper. Theoretical analysis and experimental results show the simplicity and generality of the proposed strategy.