The dynamic process of Ne-CuBr UV laser in nanosecond pulsed longitudinal discharge is analyzed, and a comprehensive self-consistent physical model is developed. The temporal evolutions of discharge parameters, main particle densities, electron and gas temperatures, and the laser pulse intensity are numerically calculated. The process of population inversion between the upper and the lower laser levels as well as the lasing mechanism are illustrated. The influences of the tube radius and discharge parameters on the laser output characteristic are also explained quantificationally.