In this paper, an axial-flux permanent-magnet (PM) vernier machine with triple-stator, spoke-type PM rotor, and toroidal winding only wound on inner stator is proposed. The quasi-3D finite element analysis (FEA) is adopted to optimize the design parameters, such as the inner stator diameter, PM thickness, and slot opening width. A 24-slot 44-pole optimized model is built in this paper and the 3D FEA is applied to validate the accuracy of the quasi-3D FEA. The results show that the torque densities of the proposed machine are 49.4 Nm/L and 11.4 Nm/kg, respectively, under the average electrical loading of 232 A/cm. The comparison to other axial-flux PM vernier machine is conducted by the 3D FEA, and the results reveal the proposed machine has the great advantages of the torque density and power factor.