This paper deals with positive and negative corona discharge in atmospheric air using a wire-to-plane system. The Poisson's equation is solved numerically using the finite-element method and the current continuity equation. The space charge density is updated using the simplified method of characteristics, where the ion diffusion is neglected. The numerical model takes into account the avalanche length of the corona discharge and the potential corresponding to the minimum ionisation field is directly introduced in the method on the border of the ionisation region. The end geometry of the linear biased probe without wraparound bias plates has been adapted to a wire-to-plane system for use in DC corona discharge. The current density and the electric field are measured; their spatial distributions are given and compared with the computed values. The agreement between the calculated values and those obtained experimentally is satisfactory. The per unit electric field and current density are also represented by a unique function.