In this paper, we investigated mass transfer of Fe^<2+> ions adjacent to the magnetite (Fe_3O_4) solid surface from the microscopic viewpoint by using the molecular dynamic simulations. Not only mass transfer characteristic across the interface, but also that along the interface has to be elucidated in order to predict the strict transport path and diffusion process of ions in the vicinity of the interface. Therefore, we here evaluated two-dimensional free energy surface along the interface according to the ion translation. With Fe^<2+> ions fixed at a certain surface separation distance (SSD), the umbrella sampling/WHAM (weighted histogram analysis method) procedure which can be applied to two-dimensional space was adopted for free energy calculations. As a result, it was found that the free energy surface is significantly influenced by the surface charge distribution of the magnetite surface.