Despite significant success in developing various periodic composites, the challenge remains how to more efficiently design the base cell so that one or more physical properties can be attained. In this paper, the material design problem is formulated in a form of the least square of the difference between the targeted and designed values. By minimizing the objective subject to volume constraints and periodic boundary conditions, an optimal material distribution in base cell can be generated. Different from existing methods, this paper shows how to use the Evolutionary Structural Optimization (ESO) method to design composite material attaining to thermal conductivity defined by the Hashin-Strikman (H-S) bounds. The effectiveness of this method is demonstrated through several 2D examples, agreeing well with commonly known benchmarking microstructures.