In this paper, on the basis of complex variable moving least squares approximations, a new complex variable moving least squares interpolating (CVMLSI) method is proposed. In this method, a complete basis function and singular weight function are introduced to form the new basis function through orthogonalization process. Then a new interpolating shape function is derived, which satisfy the property of Kronecker δ function.

Combining the CVMLSI method with the weak integral form of the two-dimensional transient heat conduction problem, a complex variable element free Galerkin interpolating (CVEFGI) method for transient heat conduction problem is obtained. Due to the fact that the essential boundary conditions can be applied directly, the final discrete matrix equation is more concise than that in the non-interpolating complex variable element free Galerkin method. Finally, a numerical example is presented to illustrate the advantages of the CVEFGI method.