A numerical study of a nitrogen cold plasma created by a pulsed discharge in a point-to-plane geometry at 4 torr is presented. The relative model is based on fluid description of the cold plasma, on Poisson's equation for the electric field and on balance equations for the excited population concerning only some vibrational band of molecular nitrogen (C3∏u, B3∏g and A$^3\sum_{\rm u}^+$). Secondary ionization phenomena and longitudinal diffusion effects are included in the model and their contribution to the glow-discharge establishment is studied. Results for space and time variations of the charged particles, electric field, potential and electronic current densities are reported. Particular attention was paid to the physical factors forming the cathodic layer and influencing its evolution. Results concerning the influence of the electronic current density on the creation of excited (radiative and metastables) particles are presented. According to these results, the plasma of the glow discharge occurs by means of three successive sequences with different characteristics. During the first sequence the gap is slowly filled of ions formed close to the anode, then in the second one an ionizing front formed close to the anode is propagating towards the cathode with an average velocity of 2 × 106 cm/s. It forms the cathodic layer zone and starts the participation of the secondary ionization effects leading to the third sequence which deals with the glow discharge establishment. The first significant production of excited states occurs within the ionizing front but the most important one is obtained when the glow discharge is established. It has been shown that at 4 torr and a gap of 1 cm, a mean electronic current density of 5 mA/cm2 is sufficient to create 109 cm−3 of (B3∏g, v = 0), 108 cm−3 of (C3∏u, v = 0) and 1011 cm−3 of (A$^3\sum_{\rm u}^+$, v = 0 ) excited particles.