Theory and results of mathematical modeling of a glow discharge in a parallel-plate configuration with axial magnetic field is presented. The model consists of continuity equations for electron and ion fluids, the Poisson equation for the self-consistent electric field. Numerical simulation results are presented for two-dimensional glow discharge at various initial conditions. The results are obtained for molecular nitrogen at pressure 1-5 Torr, emf of power supply 1-2 kV, and magnetic field induction B = 0-0.5 T.It is shown that in the presence of the axial magnetic field the glow discharge is rotated around its axis of symmetry. Nevertheless it is shown that in the investigated range of discharge parameters in an axial magnetic field the law of the normal current density is retained.