A method of removing moisture efficiently in the gas supply system by evacuation at normal temperature without using the baking method. The method involves flowing a gas to remove moisture in the gas supply system with the flow pressure of the gas to remove moisture set at not lower than a minimum pressure at which the gas flow becomes viscous and not higher than a water saturated vapor pressure at a flow temperature of the gas to remove moisture. The gas to remove moisture achieves a viscous flow when a mean free path of gas molecules is smaller than a diameter of piping of the gas supply system. If the gas for removing moisture is evacuated at normal temperature under such conditions, the adsorbed moisture on an inside surface of the piping and in the valves and filters can be removed effectively.