Worldwide, electrostatic precipitators (ESP) have been extensively utilized to separate fine particles for diverse large-scale industrial applications. In this regard, this paper presents a novel approach for modeling the dust-loaded ESP on the fine computational domain where the need for a fast solver arises. Unlike the previously published numerical techniques, the finite difference method (FDM) integrated with a full multi-grid method (FMG), labeled FDM-FMG, is developed to resolve Poisson and continuity equations on one fine computational domain. For clean and dust-loaded ESP, the proposed FMG is checked versus successive over-relaxation (SOR) on fine domains where the proposed one is greatly transcendent in terms of convergence characteristics and hence the computational performance (CPU time). For the first time, two major issues are highlighted and solved: the first concerning issue is the chosen ion mobility as an important factor in the simulation results and the second one is choosing an optimal computational grid for dust loaded precipitators that grantees both low truncation and roundoff errors, results in well-matched with experimental measurements nominated in the previous publishing. The novel idea of working on various grid sizes and tracking the optimal ones gives the FDM-FMG an advantage of predicting a precise picture for the electrical situations in industrial ESP over the other numerical techniques. After all, the impact of changing the spacing between the different wires and the height of the ionized wires on the distributions of current, ion, and particle charge densities on the ground are deeply simulated and presented in dust-loaded ESP. The proposed FDM-FMG can be a promising tool for the designers and manufacturers of precipitators, thanks to its superior computational performance.