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In this paper, a novel dual flux modulation (DFM) machine with consequent-pole spoke-array permanent magnets (PMs) in both stator and rotor is proposed to achieve a larger torque density than regular flux modulation machines. The stator has two portions of PMs, one is set next to the stator slot with circumferential magnetization, and the other is inserted between the stator yoke and flux bridge with radial magnetization. The rotor has consequent-pole spoke-array PMs and alternative flux bridges. The proposed DFMPM machine can be regarded as the combination of the flux switching PM (FSPM) machine and vernier PM (VPM) machine. First, the structure and operational principle are introduced. Then, the proposed 12-stator-slot/10-rotor-tooth dual flux modulation permanent magnet (DFMPM) machine is compared with the FSPM machine and VPM machine in terms of flux lines distribution, back-electromotive force (EMF), cogging torque and average torque. Finally, the four proposed DFMPM machines are optimized for maximum average torque and minimum ripple torque considering the effects of split ratio, slot opening ratio, PM depth, PM angle and iron angle.