The kinetic process of Cu(+) UV laser in Ne-CuBr longitudinal pulsed discharge is analyzed and a comprehensive self-consistent physical model is developed. The temporal evolutions of discharge parameters, main particle densities, the electron temperature, and the laser pulse intensity are numerically calculated. The model results illustrate the process of population inversion and the lasing mechanism. The calculations on the influences of the tube radius and Br atoms on the laser output characteristic well explain the experimental results.