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The self-potential (SP) method is one geophysical method useful for estimating properties of groundwater flow. The effect of a permeability anomaly on a SP profile has been discussed in the literature, but neither the feasibility of using SP measurements to estimate the permeability structure nor the resolution of the inversion results of an SP profile have been given much attention. In this study, we developed a two-dimensional inversion code for the estimation of permeability structure. We applied this inversion to a synthetic SP profile on the ground surface affected by the permeability structure to evaluate the resolution of the SP inversion. Four models, which include a permeability anomaly located in the center of a slope, are used for the evaluation of the inversion performance. A priori data, including the distribution of the streaming current coefficient, electrical conductivity and flux volume at the discharge and recharge, are input to the inversion. A horizontal zone with high permeability and a vertical zone with low permeability can be reconstructed using the inversion. However, the horizontal low permeable zone and the vertical high permeable zone cannot be imaged clearly. The regional groundwater flow pattern around the permeability anomaly has a great effect on the SP pattern at the surface. For an accurate inversion of SP data, it is necessary that the inversion process consider the effect of flow pattern around the permeability anomaly on the SP profile.