Abstract: By means of the asymptotic method, the two-order two-scale asymptotic expansions coupled with boundary layer of the electrical potential and the displacement were built for the structures of general periodic composites under piezoelectric condition, the coupled relation between the displacement field and the electric field within basic cell is given, and the finite element method and the algorithm of two-scale coupled with boundary layer of the displacement and the electrical potential are presented. The effectiveness and high efficiency is shown by some simple numerical examples.