Electric machines with high torque density are needed in many applications, such as electric vehicles, electric robotics, electric ships, electric aircraft, etc. and they can avoid planetary gears thus reducing manufacturing costs. This paper presents a novel axial-radial flux permanent magnet (ARFPM) machine with high torque density. The proposed ARFPM machine integrates both axial-flux and radial-flux machine topologies in a compact space, which effectively improves the copper utilization of the machine. First, the radial rotor can balance the large axial forces on axial rotors and prevent them from deforming due to the forces. On the other hand, the machine adopts Halbach-array permanent magnets (PMs) on the rotors to suppress air-gap flux density harmonics. Also, the Halbach-array PMs can reduce the total attracted force on axial rotors. The operational principle of the ARFPM machine was investigated and analyzed. Then, 3D finite-element analysis (FEA) was conducted to show the merits of the ARFPM machine. Demonstration results with different parameters are compared to obtain an optimal structure. These indicated that the proposed ARFPM machine with Halbach-array PMs can achieve a more sinusoidal back electromotive force (EMF). In addition, a comparative analysis was conducted for the proposed ARFPM machine. The machine was compared with a conventional axial-flux permanent magnet (AFPM) machine and a radial-flux permanent magnet (RFPM) machine based on the same dimensions. This showed that the proposed ARFPM machine had the highest torque density and relatively small torque ripple.