An apparatus for measuring the flow rate of water vapor in a process gas including steam includes a sample system having a dew point meter and a pressure meter, and an inert gas supply device for mixing an inert gas with a process gas in the sample system. The process gas comprises a first gas, such as natural gas, and steam. A partial pressure calculating unit calculates the partial pressure of the water vapor contained in the gas mixture on the basis of the dew point of the mixture measured by the dew point meter and the pressure measured by the pressure meter. A flow rate calculating unit calculates the flow rate of the steam contained in the process gas on the basis of the water vapor partial pressure, the inert gas flow rate, and the flow rate of the first gas in the process gas.