Abstract : Biochemical networks are the backbones of physiological systems of organisms. Therefore, a biochemical network should be sufficiently robust (not sensitive) to tolerate genetic mutations and environmental changes in the evolutionary process. In this study, based on the robustness and sensitivity criteria of biochemical networks, the adaptive design rules are developed for natural selection in the evolutionary process. This will provide insights into the robust adaptive mechanism of biochemical networks in the evolutionary process. We find that if a mutated biochemical network satisfies the robustness and sensitivity criteria of natural selection, there is a high probability for the biochemical network to prevail during natural selection in the evolutionary process. Since there are various mutated biochemical networks that can satisfy these criteria but have some differences in phenotype, the biochemical networks increase their diversities in the evolutionary process. The robustness of a biochemical network enables co-option so that new phenotypes can be generated in evolution. The proposed robust adaptive design rules of natural selection gain much insight into the evolutionary mechanism and provide a systematic robust biochemical circuit design method of biochemical networks for biotechnological and therapeutic purposes in the future.