A pressure regulator (1; 41), characterised by: a servo valve for regulating an inflow rate of a compressive fluid to be supplied from a compressive fluid supply source; an isothermal pressure vessel for isothermally maintaining the compressive fluid flowing into the isothermal pressure vessel via the servo valve; a pressure detection means for detecting a pressure of the compressive fluid in the isothermal pressure vessel; a pressure differential value detection means for detecting a pressure differential value of the compressive fluid in the isothermal pressure vessel; and a pressure control means for controlling a pressure of the compressive fluid in the isothermal pressure vessel at a predetermined pressure by operating the servo valve, wherein the pressure control means includes: a pressure control system (20; 50) for feedback-controlling the pressure detected by the pressure detection means; an inflow rate control system for feedback-controlling the inflow rate of the compressive fluid flowing into the isothermal pressure vessel; and an outflow rate estimating means (27; 57) for estimating an outflow rate of the compressive fluid flowing out from the isothermal pressure vessel based on the pressure differential value detected by the pressure differential value detection means, wherein a model follow-up control system (28; 58) for feeding back the outflow rate estimated by the outflow rate estimating means to the inflow rate control system is configured in a control loop of the pressure control system. a servo valve for regulating an inflow rate of a compressive fluid to be supplied from a compressive fluid supply source; an isothermal pressure vessel for isothermally maintaining the compressive fluid flowing into the isothermal pressure vessel via the servo valve; a pressure detection means for detecting a pressure of the compressive fluid in the isothermal pressure vessel; a pressure differential value detection means for detecting a pressure differential value of the compressive fluid in the isothermal pressure vessel; and a pressure control means for controlling a pressure of the compressive fluid in the isothermal pressure vessel at a predetermined pressure by operating the servo valve, wherein the pressure control means includes: a pressure control system (20; 50) for feedback-controlling the pressure detected by the pressure detection means; an inflow rate control system for feedback-controlling the inflow rate of the compressive fluid flowing into the isothermal pressure vessel; and an outflow rate estimating means (27; 57) for estimating an outflow rate of the compressive fluid flowing out from the isothermal pressure vessel based on the pressure differential value detected by the pressure differential value detection means, wherein a model follow-up control system (28; 58) for feeding back the outflow rate estimated by the outflow rate estimating means to the inflow rate control system is configured in a control loop of the pressure control system. a pressure control system (20; 50) for feedback-controlling the pressure detected by the pressure detection means; an inflow rate control system for feedback-controlling the inflow rate of the compressive fluid flowing into the isothermal pressure vessel; and an outflow rate estimating means (27; 57) for estimating an outflow rate of the compressive fluid flowing out from the isothermal pressure vessel based on the pressure differential value detected by the pressure differential value detection means, wherein a model follow-up control system (28; 58) for feeding back the outflow rate estimated by the outflow rate estimating means to the inflow rate control system is configured in a control loop of the pressure control system.