In this paper the wave approach is used for analysing the ECR amplifier, its dispersion relation is derived, but it is suitable only for the small signal regime. Then by using kinetic power conservation theorem, a theoretical analysis is employed to treat this amplifier, it can be applied beyond the small signal regime to calculate the saturated output power and efficiency of this device. For a concrete waveguide form, the performence of the amplifier has been calculated numerically. The theoretical results show that the amplifiers of this type exhibit an obvious advantage, i.e. the variation of static magnetic field has less influence on its output power, besides, in comparison with the amplifier with a regular waveguide under the condition of same output powers and gains, this amplifier has a wider bandwidth and its interaction length is somewhat shortened.