A multi-phase reluctance electric motor with transverse magnetic flux which includes a stator and a rotor. The stator comprises a housing (1) and a number m of phase armature units, each being staggered at an electrical angle of 360°/m along the circumferential direction sequentially in the housing (1) along the axial direction and comprises an armature iron core, an armature coil (2) and permanent magnets (3). The armature coil (2) is embedded within an annular space formed among first, second and third annular iron core segments (6, 7, 8) of the armature iron core. The pole distance τm between two adjacent permanent magnets (3) on the same segment and the tooth distance τp between the rotor teeth (5) along the circumferential direction fulfil 2 τm=τp. This motor eliminates mutual inductance between phases, improving control precision of current and electromagnetic torque and dynamic characteristics of the system.