This paper presents a self-consistent nonlinear theory of the current and energy modulations when an electron beam propagates through an inductively-loaded wide gap cavity.The integro-differential equations are obtained to describe the modulation of the beam current and kinetic energy.A relativistic klystron amplifier (RKA) model is introduced, which uses an inductively-loaded wide gap cavity as an input cavity. And a numerical code is developed for the extended model based on the equations, from which some relations about the modulated current and modulated energy are numerically given.