A control method of controlling a wire electrical discharge machine machining a workpiece by generating electric discharge at a discharge gap between the workpiece and a wire electrode, the wire electrical discharge machine comprising: a discharge induction circuit configured to apply a discharge induction voltage across the discharge gap; and a main discharge circuit configured to supply machining current to the discharge gap, the control method comprising: a discharge gap state determining step of determining which state a discharge gap state is when the discharge induction voltage is applied across the discharge gap, among a normal state in which electric discharge occurs at the discharge gap, a short-circuited state in which the discharge gap is short-circuited and an open state in which no current flows through the discharge gap, based on a voltage across the discharge gap when the discharge induction voltage is applied across the discharge gap; a discharge gap state recording step of recording at least one of the normal state, the short-circuited state and the open state as the discharge gap state; a machining current setting step of setting a magnitude of a normal machining current depending on the discharge gap state that occurred when the discharge induction voltage was applied to the discharge gap at a previous time or previous times; and a machining current controlling step of controlling the main discharge circuit so as to supply the normal machining current to the discharge gap when the discharge gap state at a present application of the discharge induction voltage is the normal state, control the main discharge circuit so as to supply a short-circuit machining current smaller than a predetermined current to the discharge gap when the discharge gap state at the present application thereof is the short-circuited state, and control the main discharge circuit so as not to supply any machining current to the discharge gap when the discharge gap state at the present application thereof is the open state, characterised in that the discharge gap state recording step records at least the open state; and the machining current setting step sets the normal machining current to be greater than the predetermined current at least when the discharge gap state at the previous time was the open state. a discharge gap state determining step of determining which state a discharge gap state is when the discharge induction voltage is applied across the discharge gap, among a normal state in which electric discharge occurs at the discharge gap, a short-circuited state in which the discharge gap is short-circuited and an open state in which no current flows through the discharge gap, based on a voltage across the discharge gap when the discharge induction voltage is applied across the discharge gap; a discharge gap state recording step of recording at least one of the normal state, the short-circuited state and the open state as the discharge gap state; a machining current setting step of setting a magnitude of a normal machining current depending on the discharge gap state that occurred when the discharge induction voltage was applied to the discharge gap at a previous time or previous times; and a machining current controlling step of controlling the main discharge circuit so as to supply the normal machining current to the discharge gap when the discharge gap state at a present application of the discharge induction voltage is the normal state, control the main discharge circuit so as to supply a short-circuit machining current smaller than a predetermined current to the discharge gap when the discharge gap state at the present application thereof is the short-circuited state, and control the main discharge circuit so as not to supply any machining current to the discharge gap when the discharge gap state at the present application thereof is the open state, characterised in that the discharge gap state recording step records at least the open state; and the machining current setting step sets the normal machining current to be greater than the predetermined current at least when the discharge gap state at the previous time was the open state.