A pressure regulator for controlling pressure with high response and high accuracy even a flow change occurs on the downstream side. The pressure regulator (1) regulates the rate of inflow into an isothermal pressure vessel (13) for the gas supplied from a gas supply source (10) by means of a servo valve (11) to maintain the constant pressure in the isothermal pressure vessel (13). Pressure control means (a computer (16)) operating the servo valve (11) has as a main loop a pressure control system for feedback-controlling the pressure in the isothermal pressure vessel (13) measured by a pressure gauge (14) and has therein a rate-of-inflow-control system for feedback-controlling the rate of flow measured by a flow meter (12), an observer for estimating the rate of outflow from the isothermal pressure vessel (13) according to the rate of inflow and the derivative of the pressure in the isothermal pressure vessel (13) measured by a pressure differentiator (15), and a model follow-up control system for feed-backing the estimated rate of outflow to the rate-of-inflow control system.