Due to the advantage of high torque density, vernier permanent magnet (VPM) machines attract much attention in the field of low-speed direct drive. In order to further improve the performance, this paper presents a fluxfocusing axial-flux consequent-pole VPM (FF-AFCPVPM) machine. Firstly, the basic structure of the machine is described, which has a yokeless and segmented armature, fractional slot concentrated winding and double rotors. Then, the equivalent air gap length is derived to obtain the magnetic flux density after tooth chamfering, and the improvement mechanism of torque and power factor is studied. In order to face more practical industrial applications, the optimization of single tooth chamfering and global tooth chamfering is studied. Finally, the validity of the proposed machine structure is demonstrated by finite element analysis (FEA). The results show that different teeth have their optimal tooth chamfering, which can improve torque density and power factor, and reduce cogging torque.