In response to violent market competition and demand for low-carbon economy, cold chain logistics companies have to pay attention to customer satisfaction and carbon emission for better development. In this paper, a biobjective mathematical model is established for cold chain logistics network in consideration of economic, social, and environmental benefits; in other words, the total cost and distribution period of cold chain logistics are optimized, while the total cost consists of cargo damage cost, refrigeration cost of refrigeration equipment, transportation cost, fuel consumption cost, penalty cost of time window, and operation cost of distribution centres. One multiobjective hyperheuristic optimization framework is proposed to address this multiobjective problem. In the framework, four selection strategies and four acceptance criteria for solution set are proposed to improve the performance of the multiobjective hyperheuristic framework. As known from a comparative study, the proposed algorithm had better overall performance than NSGA-II. Furthermore, instances of cold chain logistics are modelled and solved, and the resulting Pareto solution set offers diverse options for a decision maker to select an appropriate cold chain logistics distribution network in the interest of the logistics company.