Based on the linear theory of gyrotron, and using the Laplace transformation and residue theorem, the kinetic theory of a novel gyrotron with three-mirror quasi-optical cavity is developed within the framework of the linearized Vlasov-Maxwell equations. The beam-wave interaction power, frequency shift and starting current have been derived and numerically calculated. The results indicate that this novel gyrotron has high interaction power when operating at high cyclotron harmonics, and has potential application in THZ band.