An axial-flux permanent-magnet (PM)-assisted claw-pole generator (APCG) is designed based on an equivalent magnetic circuit model (EMCM). It is designed for generating power in vehicle with the merits of high power density, no brush, and wide airgap flux density modulation range. This paper mainly focuses on establishing the EMCM of the APCG and designing a set of optimal structure parameters. First, the topology and operation principle of the APCG are introduced in detail, including material, fabrication, and magnetic flux distribution. Second, the magnetic circuits in claw poles are simplified and the relationships among the key parameters are discussed. Finally, based on the simplified model and the relationships among the key parameters, the EMCMs of current and PM excitation are established, respectively. According to the EMCM, a scheme of a 4 kW APCG is carried out. Comprehensive investigations demonstrate that the EMCM is time-saving and relatively accurate when compared with a finite element method.