In consideration of the thickness and the relativistic effect of the hollow electron beam, the hot dispersion relation including the electron beam space charge effect for the ring plane traveling wave tube was derived by making use of the Ritz Galerkin method and combining with the field matching method. The numerical results given were in terms of the small signal gain curve. Finally, the influences of the radius and current of the electron beam, the acceleration voltage and the geometrical dimensions of the slow wave structure on the small signal gain were discussed. The results presented in this paper provide theoretical basis on designing the millimeter wave ring plane traveling wave tube.