This paper concerns computational modelling of the low-temperature glow discharge plasma in the atmospheric pressure helium after spark breakdown and research on the dependence of a spatial distribution of plasma on the initial conditions of discharge and parameters of the external electric circuit. This study analysed the influence of the initial distribution of a space charge on the generation of the glow discharge plasma after the spark breakdown between flat electrodes by means of a 2D-axial symmetric model of the atmospheric pressure helium plasma in the drift-diffusion approximation. With the discharge current of 1–12 mA, the solution for a quasi-steady state of plasma is obtained. The dependence of a type of this discharge mode on the parameters of the external electric circuit and coefficient of the secondary cathode emission is studied.