A novel approach for solving the monopolar corona in high voltage direct current (HVDC) transmission line systems is proposed by the finite difference method (FDM) and a full multigrid method (FMG). Specifically, the FMG is implemented as a fast solver with respect to existing iterative solutions for the FDM to solve the Poisson equation, particularly on fine grids. The advantage features of the proposed approach are that it avoids the hypothesis of a constant electric field around the conductor's surface. Further, it considers the influence of space charge on both the magnitude and the direction of the electrical field. The proposed approach is employed for computing the electric field and current density on the ground plane with and without wind effect. Considering the impact of wind in the present study, the findings confirm that both corona current density and electric field on the ground plane are influenced by the transverse wave. Eventually, the effect of changing the wind speed on the electric field profiles and the current density is deeply studied in HVDC transmission line systems. To prove the efficacy of the proposed approach, it is compared with previous experimental results where a better agreement is reached rather than other numerical techniques.