This paper presents a concurrent topology optimization method to simultaneously achieve the optimum structure and material microstructure for minimum system compliance. Microstructure is assumed to be uniform in macro-scale to meet manufacturing requirements. Design variables for structure and material microstructure are independently defined and then integrated into one system with the help of homogenization theory. Penalization approaches are adopted in both scales to ensure clear topologies, i.e. SIMP (Solid Isotropic Material with Penalization) in micro-scale and PAMP (Porous Anisotropic Material with Penalization) in macro-scale. Numerical experiments for two examples validate the proposed method and also demonstrate the superiority of truss-like materials.