In pulse welding apparatus of arc welding or short-circuit transfer type arc welding in which a pulse discharge created on the tip of a wire electrode is utilized to perform welding, when a molten droplet produced on the tip of wire electrode is late to separate from the wire due to variations of welding conditions and external disturbances. The wire-supplying speed at which the wire is supplied to the weld zone changes. This causes undercut, i.e., a defect in welding bead-shape that presents adverse effect to welding quality. To prevent this problem, pulse current supplied to the base metal is divided into a plurality of pulse groups and the average current reaches the maximum peak value at a predetermined time after beginning of outputting the pulses, and the group of pulse currents is of a hill-shape in its envelope in accordance with the separation phenomenon of molten droplet, and the group of pulse currents is arranged to have different pulse period, pulse width, and pulse interval. In the sort-circuiting arc welding, the short-circuit and arc are instantly controlled in accordance with the detected arc length or wire-supplying speed.