Abstract: Starting from the relativistic motion equation and the energy equation of the electron, a large-signal theory which describes the beam-wave interaction of the gyro-peniotron for arbitrary TEmn mode and arbitrary harmonic of the cyclotron frequency is presented. Numerical simulation shows that under defined conditions an electronic efficiency of about 45% for the third cyclotron harmonic at an operation frequency of 35 GHz could be obtained, while the required DC magnetic field is only 4.2 kGs. This fact indicates that this device could be efficiently operated at high efficiency and low magnetic field. Therefore, the practical application of the gyro-device will be greatly exended and the potential for sort-millimeter and sub-millimeter wavelength exists.