A power supply apparatus for a resistance welder has an inverse-parallel thyristor circuit for constrolling the welding current. One of thyristors connected in inverse-parallel relationship is turned on by a first signal whose reference phase is established by a synchronizing signal which is based on a voltage wave form of an AC power source and the other thyristor is turned on by a second signal whose reference phase is established by a signal which is delayed half a period of the voltage wave form with respect to the first signal, so that integrals of positive and negative halves of the output voltage wave form of the inverse parallel thyristor circuit can always be made equal.