Abstract: To obtain the optimal topological configuration for thermal conductive microstructures of composite materials, a topological optimization model of the periodic structure is established by the Independent Continuous Mapping method. In this model, minimized weight is taken as the objective and thermal compliance is the constraint condition. The thermal compliance constraint is approximately formulated using a first-order Taylor expansion. The image-filtering method is implemented by a partial differential equation to eliminate checkerboard patterns and mesh-dependence problems. To satisfy the periodic constraint, the designable domain is divided into a certain number of identical subdomains and the contribution coefficients of thermal compliance are redistributed. Optimal topological configurations with different periodic numbers and different loading conditions are compared and analyzed. Numerical results verify the validity of the proposed topology optimization method in designing the microstructures of composite materials for thermal conduction.