An axial field flux-switching permanent magnet machine (AFFSPMM) is suitable to be used in wind power generation and electric vehicles. But the cogging torque (Tcog) is large. For obtaining high performance AFFSPMM, the reduction of Tcog in AFFSPMM is investigated. The theoretical Tcog expression is deduced. Based on 3-D finite element method, the influences of the design parameters on the Tcog and the reduction methods of Tcog, such as rotor tooth skewing (RTS), rotor tooth circumferential pairing (RTCP), and rotor tooth notching (RTN), are analyzed. The design parameters except the axial length of rotor have influences on Tcog and optimizing the design parameters can decrease Tcog. Tcog can reduce greatly by RTS for AFFSPMM with parallel stator tooth and fan-shape permanent magnet (PST-FSPM) structure. However, RTS is no effective in reducing Tcog for AFFSPMM with fanshape stator tooth and parallel PM (FSST-PPM) structure. Tcog decreases greatly by RTN and RTCP for FSST-PPM stator structure. Moreover, the reduction effect of Tcog with RTN is better than that with RTCP.