To provide a control method of the gas supply mechanism of an artificial respirator capable of preventing the practical delay of an inspiration supporting operation and supporting a highly similar respiratory operation to the respiratory efforts of a patient.

The point Tonset of time of starting inspiration is detected and a compensation value H to be lowered with the lapse of time is generated. Then, on the basis of a compensation flow rate FH for which the compensation value H is added to a detected flow rate F, the target pressure Pin of a support gas is computed. Thus, the inspiration support operation by a gas supply servo mechanism is practically started from the point Tonset of time of starting the inspiration and the practical delay of the inspiration support operation is prevented. Also, since the compensation value H is lowered with the lapse of time, after an initial period WH elapses in an inspiration period, the influence of the compensation value H included in a compensation flow rate value FH is reduced. By reducing the influence of the compensation value H in such a manner, the inspiration support operation is prevented from becoming excessive.