Abstract: For optimal design of the composite composed of material with different Poisson's ratios, a concurrent design method for microstructures of composites and macrostructures by considering the Poisson effect was presented, when considering the macrostructure and complicated boundary conditions. A distinctive feature lies in the interpolation of Poisson's ratios for different constituent phases. The macrostructures were supposed to be constructed by periodic base composites which contains two isotropic constituent phases with distinct Poisson's ratios. The topological optimization model was established where the system compliance was minimized in static problems or the eigenvalue was maximized in dynamic problems and the macro and micro-scale volume fraction was used as constraints. The effective properties of the composites were calculated through the homogenization theory. Sensitivities on macro-and micro-scales level were derived. Density filter and sensitivity filter schemes were adopted to eliminate the instabilities in macro-and micro-scale topology optimization, respectively. The optimality criteria method was used to update both the macro-and micro-scale densities. The effect of the micro-scale volume fraction and Poisson's ratio of the constitute phases on topological results was investigated. Several 3D illustrative examples were presented to demonstrate the effectiveness and advantage of the proposed concurrent design approach.