For an electrical reluctance rotary machine, a stator has a winding as an armature, and a rotor has permanent magnet implanting slots provided in a rotor core at lateral sides magnetic poles configured to produce reluctance torque along directions of magnetic flux passing through the magnetic poles to produce reluctance torque, and permanent magnets inserted in the permanent magnet implanting slots so as to cancel magnetic flux of the armature intersecting that magnetic flux, to control a magnetic field leaking at ends of the magnetic poles, having circumferential magnetic unevenness. The electrical reluctance rotary machine is configured to meet a relationship, such that 1.6 ≤ P × W pm R ≤ 1.9 where Wpm [mm] is a width of permanent magnet, R [mm] is a radius of the rotor, and P is the number of poles.