A speed-variable field winding type of synchronous rotary electric machine is provided, where a rotor with plural-phase windings faces a rotor with a field winding. A field current is limited to flow through the field winding in one direction thereof. A fundamental component of armature current, which corresponds to a synchronizing current for producing a rotating magnetic field rotating in sync with the rotation of the rotor, is supplied to the armature windings. The synchronizing current is adjusted in frequency to change a rotor rotation speed. A pulsed rotor exciting current is supplied to the armature windings. The exciting current causes the field winding to induce the field current only during a specified current-supply duration shorter than a one cycle of the synchronizing current. The number of current-supply times for the exciting current, per electrical angle 2π and per phase, has a positive correlation with the cycle of the synchronizing current.