PurposeTo improve the output torque density of the machine and to be better suited for automation applications, this paper aims to propose a double-permanent-magnet enhanced hybrid stepping machine (DPMEHSM) with tangential and radial magnetization.Design/methodology/approachFirst, the structure of DPMEHSM is introduced and its operation principle is analyzed by describing the variation in stator poles versus time. Second, based on the similar electrical load and amount of PM, the size equations of the DPMEHSM are designed and the main parameters are presented. Third, the electromagnetic performances including the PM flux linkage distribution, magnetic density distribution, air-gap field, back electromotive force (back-EMF), detent torque, holding torque and output torque of DPMEHSM and stator-PM hybrid stepping machine (SPMHSM) are analyzed based on the finite element method.FindingsThe results show that the DPMEHSM has superiority in back-EMF, holding torque and output torque.Originality/valueThis paper proposes a DPMEHSM with tangential and radial magnetization to improve the output torque density.