A power supply for arc welding includes switching elements PTR, NTR for switching the polarity of the direct voltage from a power circuit PMC. The element PTR is connected in parallel to a series unit of a switching element TR1 and a resistor R1. Likewise, the element NTR is connected in parallel to a series unit of a switching element R2 and a resistor R2. A necking determination circuit ND determines whether a constriction occurs at the molten bridging portion between the welding wire and the base material. When the constriction occurs during the "electrode positive" mode, the switching element PTR is turned off, while the switching element TR1 is brought into the conduction state. When the constriction occurs during the "electrode negative" mode, the switching element NTR is turned off, while the switching element TR2 is brought into the conduction state.