A new mesh refinement approach on h-adaptation for FEM is discussed in this paper. Since there are some limitations in the r-method, especially for problems with rather complicated domains, h-refinement was supposed to be an alternative for such problems. An ordinary local remeshing approach in the h-method has a great difficulty in controlling the mesh size depending on the error measures. As a result, the number of elements is very easily increased, and the computational efficiency in FEM is decreased. The purpose of our global remeshing scheme reported in this paper is to solve these problems. Our approach can be summarized as follows: generate subdomain data based on error measure, input these data into the automatic mesh generator which supports the subdomain data structure, then get very smooth and controlled refined meshes. Its effects are evaluated with several examples on both stress concentration problem and conductive heat transfer problem.