Sinusoidal back-EMF waveform of vernier Permanent Magnet (PM) machines is analyzed in this paper. An analytical expression of Electromotive Force (EMF) of electric machines including vernier machines is developed to analyze EMF harmonics, and the effect of vernier PM machine pole ratio, the ratio of number of rotor poles to stator poles, on the EMF waveform. Moreover, this paper represents several Finite Element Analysis (FEA) models to verify the analysis based on the proposed expression, and the effect of tooth width ratio, which is the ratio of tooth width to tooth pitch, on back-EMF of vernier PM machines, and optimal tooth width ratio is obtained and verified by FEA. Finally, this paper makes comparisons between EMF waveform of vernier PM machines and that of traditional PM machines from the point of view of analytical EMF expression.