A wire electric discharge machine comprising: a discharge inducing circuit including a first DC power supply connected to a machining gap between a wire electrode and workpiece via a first switching element and a current limiting resistance; a current supply circuit including a second DC power supply connected to the machining gap via a second switching element, the current supply circuit configurable to supply a first, larger current for discharge machining and to supply a second, smaller current so as not to fuse the wire electrode in a short-circuit state with the workpiece; a voltage detection circuit that detects a voltage of the machining gap; a short-circuit detection unit (S1, 57) that detects a short-circuit state between the wire electrode and the workpiece based on the voltage detected by the voltage detection circuit; and a control circuit that controls on and off of the first switching element and the second switching element, wherein the control circuit is configured, if the short-circuit detection unit (S1, 57) detects that there is not a short-circuit state between the wire electrode and the workpiece at the start of machining, to control the current supply circuit to supply the first, larger current for discharge machining, and wherein the control circuit is configured, if the short-circuit detection unit (S1, 57) detects that there is a short-circuit state between the wire electrode and the workpiece at the start of machining, to control the current supply circuit to supply the second, smaller current, so that the wire electrode is not fused in the short-circuit state with the workpiece, until the short-circuit detection unit (S1, 57) detects elimination of the short-circuit state, wherein the control circuit is further configured to change to preset machining conditions when the short-circuit detection unit (S1, 57) detects elimination of the short-circuit state. a discharge inducing circuit including a first DC power supply connected to a machining gap between a wire electrode and workpiece via a first switching element and a current limiting resistance; a current supply circuit including a second DC power supply connected to the machining gap via a second switching element, the current supply circuit configurable to supply a first, larger current for discharge machining and to supply a second, smaller current so as not to fuse the wire electrode in a short-circuit state with the workpiece; a voltage detection circuit that detects a voltage of the machining gap; a short-circuit detection unit (S1, 57) that detects a short-circuit state between the wire electrode and the workpiece based on the voltage detected by the voltage detection circuit; and a control circuit that controls on and off of the first switching element and the second switching element, wherein the control circuit is configured, if the short-circuit detection unit (S1, 57) detects that there is not a short-circuit state between the wire electrode and the workpiece at the start of machining, to control the current supply circuit to supply the first, larger current for discharge machining, and wherein the control circuit is configured, if the short-circuit detection unit (S1, 57) detects that there is a short-circuit state between the wire electrode and the workpiece at the start of machining, to control the current supply circuit to supply the second, smaller current, so that the wire electrode is not fused in the short-circuit state with the workpiece, until the short-circuit detection unit (S1, 57) detects elimination of the short-circuit state, wherein the control circuit is further configured to change to preset machining conditions when the short-circuit detection unit (S1, 57) detects elimination of the short-circuit state.