In this paper, the effect of flux modulation pole (FMP) number on the performance of a spoke array fault tolerant permanent magnet vernier rim driven machine (SA-FTPMV-RDM) is studied. Firstly, a hybrid stator is adopted in this machine in which armature teeth and isolation teeth are arranged alternatively, and the winding type is single-layer fractional slot concentrated winding (SL-FSCW). Spoke array magnet is employed in the rotor of the machine to achieve flux focusing effect. Then the parameter scanning method is used to optimize the FMP pitch ratio, isolation tooth width ratio, FMP height, and permanent magnet thickness under different numbers of FMPs. It is concluded that there is an optimal FMP number for 12 slots SA-FTPMV-RDM to maximize the torque. Finally, the electromagnetic performances of the optimized machines with different number of FMP are compared by using the finite element analysis (FEA). The results show that the machine with the optimal number of FMPs has the highest torque density and efficiency, strong fault tolerance, but relatively large torque ripple.