This paper presents the dual interpolation boundary face method (DiBFM) based on a binary tree grid for solving the 3-D potential problems. The subdivision method based on binary tree algorithm is capable to generate both continuous and discontinuous grids, and to achieve the grids generation for arbitrary complex model much easier and automatically. By adding virtual nodes on the vertices and edges of traditional discontinuous element, the dual interpolation elements are introduced while the order is increased by two. The values of physical variables are approximated by Lagrange interpolation polynomial in the first-layer interpolation, and meshless interpolation is used to condense the degree of freedom of virtual nodes in the second-layer interpolation. Since no requirement is needed for the continuity of grids in the DiBFM, the dilemma of discontinuous grids are avoidable. In this paper, the DiBFM is implemented based on the binary tree grids to solve general problems with thin-wall structures and “geometrical construction noise”.