Permanent　magnet　Vernier　machines　(PMVMs)　have　drawn　increasing　attention　in　recent　years　due　to　the　advantage　of　high　torque　density.　However,　the　inherent　low　power　factor　issue　of　PMVMs　remains　a　key　challenge.　In　this　paper,　a　novel　axial-flux　permanent　magnet　vernier　machine　(AFPMVM)　with　modular　stator　is　proposed.　Benefiting　from　the　unique　separation　slot　structure,　the　proposed　machine　can　obtain　not　only　the　improved　power　factor　but　also　the　higher　electromagnetic　torque,　and　this　is　explained　theoretically　by　air-gap　field　modulation　theory.　A　magnetomotive　force　(MMF)-permeance　model　is　established　to　predict　the　air-gap　field　harmonics　modulated　by　the　stator　slots.　Moreover,　by　quantifying　the　contribution　of　air-gap　field　harmonics　to　the　torque　generation,　the　working　and　non-working　harmonic　components　of　the　air-gap　field　in　the　proposed　machine　can　be　determined.　Meanwhile,　the　relationship　between　electromagnetic　torque　and　power　factor　of　the　proposed　AFPMVM　is　revealed　from　the　perspective　of　the　air-gap　field　harmonics.　Then,　the　power　factor　of　the　proposed　machine　is　significantly　improved　due　to　the　lower　non-working　harmonic　contents　of　armature　reaction　field.　The　analysis　results　show　that　the　proposed　AFPMVM　can　achieve　4.1%　higher　electromagnetic　torque　and　6.9%　higher　power　factor　than　the　existing　AFPMVM.　Finally,　the　influences　of　some　key　design　parameters　on　electromagnetic　torque　and　power　factor　of　the　proposed　AFPMVM　are　analyzed　and　verified　by　finite　element　analysis.