Permanent-magnet vernier machines (PMVMs) have attracted much attention for their high efficiency and output torque in low-speed application. However, the conventional PMVM suffers from the problems of low power factor and high cogging torque. In this paper, a double-stator flux-focusing split-pole permanent-magnet vernier machine (SP-PMVM) with low cogging torque and high power factor has been proposed. The split-pole topology in the vernier motor has been used mainly to modulate the magnetic flux in this paper, although the stator teeth are used for this purpose in some cases. The newly-proposed SP-PMVM topology is characterized by reduced flux leakage through using a flux-focusing topology and staggering approximately half of the pitch angularly between the inner stator and outer stator. Firstly, the vernier principle of the proposed SP-PMVM has been investigated by analytical methods. Secondly, a 12-slot-stator and 22-pole-pair-rotor SP-PMVM has been optimized with the goal of maximum average steady-state torque and the minimum cogging torque and ripple. Thirdly, the overall performance of the newly-proposed SP-PMVM has been analyzed as compared with the conventional PMVM. The results verify that the SP-PMVM can provide higher power factor, higher output torque and lower cogging torque than that of the conventional PMVM in low-speed application.