A self-consistent physical model describing the kinetic process of the longitudinal pulsed discharge-excited copper vapor laser was established, and numerical solutions of the model were obtained. The terminating mechanisms of the copper vapor laser pulse have been further analyzed according to the simulation results. It is shown that the important factors resulting in the termination of laser pulse are the processes of stimulated emission transition, the electron impact excitation of the lower laser level and the depopulation of the upper laser level to the higher excitation levels by electron collisions.