It is well known that structural behaviors of composite solids are determined by topology of microstructures of different sizes. In this paper a concurrent topology optimization method for integrated design of materials and structures with periodical microstructure was presented. The microstructures were assumed to be uniform in macro scale and heterogeneous in micro scale and the optimization object was to minimize the material global compliances. Design variables for structure and material microstructures were defined, independently. SIMP (Solid Isotropic Material with Penalization) was adopted to ensure clear topologies in both macro and micro scales. Design variables for structure and material microstructures were integrated into one system by using the super-element method. Influences of Representative Volume Element sizes, material ratio of macro-scale and micro-scale on structural topology are investigated. Numerical experiments validate the proposed method which can be used as an innovative design concept for the lightweight structures.