This paper presents a new method for combining finite elements with meshless methods, which increases the accuracy of computational solutions in a coarse mesh by adding nodes in the domain of interest. The present method shares the features of the finite element and meshless methods such as (a) the meshless interpolation of the MLS type is employed; (b) integration domains are consistent with support domains; and (c) essential boundary conditions can be applied directly. In the present method, a ground mesh with triangular or quadrilateral elements is constructed to define polygonal support domains, and then additional nodes are placed arbitrarily in a domain without the reconstruction of a mesh. The method is very useful in an adaptive calculation, because nodes can be easily added or removed without any remeshing process.