: This paper was concerned to simulate seepage phenomena (problems) via a novel approach. A high-resolution finite volume method (FVM) was employed to solve the two-dimensional (2D) seepage equations (SEs) using an unstructured grids. Voronoi mesh generation method has been exploited for grid generation method due to its special advantages. In this attempt, to reach to a proper accuracy, solving method obtained on even-odd steps was applied.The model named V-Seep (with MATLAB software) was run under different seepage conditions and then verified by comparing the model outputs with results obtained from different models and measured seepage. The Phase2-2D and Seep-W software which are based on FEM and a code based on FVM with triangular grids. Due to a precise agreement between those output and other software results, the V-Seep could be considered as a reliable method for dealing with seepage problems, especially in embankment dams. In addition, statistical observations indicated a good conformity between the V-Seep and measured data from a case study. The results indicated a higher efficiency and precision of the discrete equations resulted from the Voronoi mesh. Thus, it could be recommended to utilize the Voronoi mesh in the numerical discrete equations. تفاصيل المقالة