The invention is directed to apparatus for measuring mass flow-rates of the gas, oil and water phases in a wet gas, comprising the following parts: a differential pressure flow meter, having a throat section, and a gamma ray detector, comprising a gamma ray emitter and a gamma ray receiver that are arranged in such a manner that gamma rays emitted from the gamma ray emitter can pass through the throat section in diametrical direction to reach the gamma ray receiver; wherein a radioactive source in the gamma-ray emitter is a multi-energy radioactive source that can naturally emit at least three energy gamma rays, and a thermostatic device is not used in the gamma ray receiver. The invention further relates to a metering method for measuring mass flow-rates of the gas, oil and water phases in a wet gas, in which the above apparatus is used. As for the apparatus according to the invention, neither a thermostatic device nor the calibration for the empty tube value is in need, and thus it is very suitable for the uses under water or down-hole.