A gyro-peniotron effected in a centrifugal electrostatic focusing system is proposed. The perturbation solution of 3-D model for large-orbit relativistic E-beam under the action of HF field of TEmn or TMmn modes is derived. The dispersion equation and the analytic expression of normalized growth rate are obtained. Numerical analysis is carried out and it is found that the influence of the axial displacement of electron should not be ignored.