An AC excitation synchronous rotating electric machine includes a multi-phase coil, an armature core, an outer yoke core, a field-winding-less rotor and a controller. The armature core has the multi-phase coil wound thereon. The rotor is rotatably disposed so as to face the armature core and includes magnetic poles each having a facing portion and a magnetic reluctance portion. The facing portion is provided at one axial end of the magnetic pole so as to face the outer yoke core and allow magnetic flux to flow therebetween. The magnetic reluctance portion is provided at the other axial end of the magnetic pole to impede the magnetic flux from flowing therethrough. The controller controls supply of multi-phase alternating current to the multi-phase coil so that magnetomotive force generated in the armature core is applied to the magnetic poles, thereby causing the magnetic poles to operate as a DC field.