In this paper, a coaxial cavity gyrotron with inner-outer corrugation is researched. The electron kineto-equations and the first order transmission line equations of the gyrotron are derived from Lorentz force equation and the transmission line theory, respectively. And then, a 2 MW, 170 GHz coaxial cavity gyrotron with inner-outer corrugation is designed. By means of numerical calculation, the beam-wave interaction of the coaxial cavity gyrotron with inner-outer corrugation is investigated. Results show that the efficient and the outpower of the gyrotron are 42.3% and 2.38 MW, respectively.