A signal processing portion obtains the reciprocal of a composite impedance of gap static capacitance and a plasma impedance, obtains composite static capacitance which is the sum of the gap static capacitance and a static capacitance component included in the plasma impedance from an imaginary part of the reciprocal, and obtains a resistance component included in the plasma impedance from a real part of the reciprocal. A gap detection device obtains the static capacitance component by using a model representing the characteristics of the reciprocal of the plasma impedance and the resistance component and obtains the gap static capacitance by subtracting the static capacitance component from the composite static capacitance. The gap detection device obtains a gap from the obtained gap static capacitance. Thus provided is a technique to detect a gap between a nozzle of a laser beam machine for outputting a laser beam and an object to be machined with high accuracy.