The modeling of DC glow discharge in argon at the pressure p = 1.5 Torr and inter-electrode distance d = 1 cm was performed for different voltages and glow currents. For the first time, argon glow discharge is modeled using a two-dimensional (2D) fluid model with non-local ionization. A detailed numerical procedure for 2D fluid modeling is given. The 2D profiles of particle number densities and electric potential obtained from the fluid model with non-local ionization and the simple fluid model are presented and compared.