This paper proposes a novel axial-radial flux permanent magnet machine (ARFPMM). The design and optimization process for higher torque density and lower cogging torque are presented. T-type SMC core, axial rotor, and radial rotor are applied to sup-port axial-radial flux path and make full use of the space. The structure and operation principle of ARFPMM are introduced. To improve the power density, different types of radial rotor are analyzed by finite element method (FEM) and the optimal PM radial rotor is determined. To reduce the cogging torque, bidirec-tional PM skewing technique is applied. The optimal combination of skewing angle and position angle is derived. The comparison between the initial and revised model shows the effectiveness of the PM radial rotor and the bidirectional PM skewing technique in the ARFPMM. Compared with the conventional axial flux permanent magnet machine, the proposed ARFPMM shows ad-vantages in average torque and space utilization.