For high temperature applications of laminated composite structures, viscoelastic behavior of laminated composite structures is investigated by multi-scale analysis based on a homogenization theory. Effective viscoelastic properties of the laminas are evaluated by a boundary integral method at a micro-scale level, and viscoelastic analysis for laminated composite structures is performed by a finite element method at a macro-scale level using the effective viscoelastic properties of lamina obtained by the micro-scale analysis. In the multi-scale analysis, the Laplace transformation is adopted and the correspondence principle between elastic and viscoelastic solutions in the Laplace domain is applied. The inverse Laplace transform is formulated by the Duhamel integral, and is calculated numerically. As a numerical example, a laminated composite plate with a hole is treated and the viscoelastic behavior of the laminated composite structure is elucidated.