This paper aims at the analysis of the monopolar ionized field in conductor-to-plane configurations without resort to Deutsch's assumption. An iterative finite-element technique is used to solve Poisson's equation. Satisfying the current continuity condition and updating the space-charge density are based on the application of Kirchoff's current-balance law at each node of the finite-element grid and take the ion diffusion into account. The proposed method of solution has been applied for laboratory and full-scale models of monopolar transmission line. The calculated V-I characteristics, the current-density and electric field profiles at the ground plane agreed well with those measured experimentally in comparison with previous calculations. Fast convergence and simplicity in programming characterize the proposed method.