Based on the moving least‐squares (MLS) approximation, an improved interpolating moving least‐squares (IIMLS) method based on nonsingular weight functions is presented in this paper. Then combining the IIMLS method and the Galerkin weak form, an improved interpolating element‐free Galerkin (IIEFG) method is presented for two‐dimensional potential problems. In the IIMLS method, the shape function of the IIMLS method satisfies the property of Kronecker δ function, and there is no difficulty caused by singularity of the weight function. Then in the IIEFG method presented in this paper, the essential boundary conditions are applied naturally and directly. Moreover, the number of unknown coefficients in the trial function of the IIMLS method is less than that of the MLS approximation; then under the same node distribution, the IIEFG method has higher computational precision than element‐free Galerkin (EFG) method and interpolating element‐free Galerkin (IEFG) method. Four selected numerical examples are presented to show the advantages of the IIMLS and IIEFG methods.