The effect of space-charge and relativistic self magnetic-field on the self-consistent equilibrium of the system with a relativistic hollow electron beam and ion-channel is studied. The distribution function and the relationship between location and energy of electron beam are derived by use of kinetic theory. The self-consistent field in ion-channel has also been established. It is clearly shown that the self-consistent equilibrium of the system exists. The relation of location of beam and radius of ion-channel was presented using numerical calculation. The distribution of electro-magnetic field in ion-channel is also given. The theory which is used in apparatus design is afforded by the research.