The automatic wire-threading device includes a wire feed motor that drives a wire feed roller in a feeding direction, a wire-feed-motor control unit that outputs a feeding-direction rotation-speed reference to the wire feed motor at a time of a threading operation of a wire electrode and that reduces torque in a feeding direction when a detected rotation speed of the wire feed roller is larger than the feeding-direction rotation-speed reference, a wire collecting motor that drives a wire collecting roller in a collecting direction, and a wire-collecting-motor control unit that outputs a predetermined wire-collecting-roller speed reference to the wire collecting motor to collect a wire. The wire-feed-motor control unit limits torque so that an absolute value of motor torque in a winding-back direction of a wire feed roller is smaller than an absolute value of motor torque in a feeding direction.