Application of a three-phase to single-phase matrix converter (MC) to a 1 kW household gas engine cogeneration system is investigated from the viewpoint that the MC can improve the efficiency of a synchronous generator with power factor control and reduce the converter losses by using reverse blocking devices. Since the MC connects a three-phase generator to single phase utility and has no energy storage component in itself, the power pulsation due to single phase power appears on the three phase side directly. To solve this problem, we have proposed a novel method to modulate the instantaneous three-phase power synchronously with the single-phase power and absorb the power pulsation with the inertia of the rotor of the generator. This proposed method was demonstrated through experiments. Efficiencies of the generator and MC were evaluated through measurements.