A theoretical and experimental study of a Penning recombination laser operating in the negative glow plasma of a pulsed high-voltage hollow cathode discharge at intermediate pressures is presented. A detailed kinetic model of the plasma - chemical reactions and radiative processes determining the inversion population on the transition is developed and the time-dependent behaviour of both the plasma and laser parameters (excited states populations, electron and ion densities, electron and gas temperatures, output power and gain) is numerically calculated. An extended experimental investigation of the main plasma and laser parameters is made and a comparison with theoretical results is presented.