This paper considers the frequency-quadrupling three-cavity gyroklystrons with successive frequency-doubling in each cavity.The cavities of 225 GHz frequency-quadrupling gyroklystron are designed with the scattering matrices method and the possible operating mode are discussed.With the point-gap theory,the starting currents of the possible operating modes and the potential parasitic modes in the output cavity are calculated.The optimal operating mode is proposed under consideration of the mode competition and the power capacity of the cavity. This paper considers the frequency-quadrupling three-cavity gyroklystrons with successive frequency-doubling in each cavity. The cavities of 225 GHz frequency-quadrupling gyroklystron are designed with the scattering matrices method and the possible operating mode are discussed. W the the point-gap theory , the starting currents of the possible operating modes and the potential parasitic modes in the output cavity are calculated. The optimal operating mode is proposed under consideration of the mode competition and the power capacity of the cavity.