A dual interpolation boundary face method (DiBFM) is presented for solving three-dimensional potential problems. The DiBFM is an alternative implementation of the boundary face method (BFM) and inherits all the merits of BFM, which has been proposed to unify the continuous and discontinuous elements, improve the accuracy of the interpolation calculation and alleviate the heavy task of mesh generation. The DiBFM implementation is based on a new type of elements, called the dual interpolation elements, in which the nodes are classified into virtual nodes and source nodes. Despite the introduction of virtual nodes in the dual interpolation elements, only source nodes of each element are taken as the collocation points. Corresponding constraint equations using the MLS approximation are formulated to condense the degrees of freedom for all virtual nodes, which does not result in the scale of final linear system increasing. In addition, even with some irregular elements in numerical simulation, accurate results and high convergence rates can be achieved by the DiBFM. The DiBFM is flexible and convenient to handle more complicated, real world structures without any geometric simplification in a fully automated manner. Numerical results have demonstrated the validity, high accuracy and superior convergence of the proposed method. (C) 2019 Elsevier Ltd. All rights reserved.