For developing a novel high-current, long pulsewidth electron source, the theoretics and mechanism of the hollow cathode plasma electron-gun are analyzed in detail in this paper, the structure and the physical process of hollow cathode pl asma electron-gun are also studied. This gun overcomes the limitations of most high-power microwave tubes, which employ either thermionic cathodes that produce low current-density beams because of the limitation of the space charge, or f ield-emission cathodes that offer high current density but provide only short pu lsewidth because of plasma closure of the accelerating gap. In the theories stud ying on hollow cathode plasma electron-gun, the characteristic of the hollow-cat hode discharge is introduced, the action during the forming of plasma of the sti mulating electrode and the modulating anode are discussed, the movement of elect rons and ions and the primary parameters are analyzed, and the formulas of the e lectric field, beam current density and the stabilization conditions of the beam current are also presented in this paper. The numerical simulation is carried o ut based on Poisson's equation, and the equations of current continuity and move ment. And the optimized result is reported. On this basis, we have designed a ho llow-cathode-plasma electron-gun, whose output pulse current is 2kA, and pulse w idth is 1 microsecond.