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Energy internet zones (EIZ) supply multiple energy carriers to customers in certain regions. They can achieve high energy efficiency by energy cascade utilization. In mid‐term, they participate in the wholesale market and retail market simultaneously. Customers can shift their energy use among different hours and energy carriers to satisfy demand according to the retail prices. Unfortunately, multiple energy systems and markets bring various uncertainties on demand and prices. In this paper, the weekly bidding strategy for the EIZ is proposed to determine the optimal bilateral contracts to sign and the optimal energy retail prices. In retail market, the satisfaction degree and elasticity matrix describe customers' response. Distributionally robust optimization is adopted to consider the distributional uncertainties of random variables and Worst‐case Conditional Value‐at‐Risk is employed for risk management. The distributional uncertainties of pool prices and elasticity matrix are discussed in this paper. An EIZ in Shanghai, China is adopted to illustrate the proposed strategy. The results have great resistance to distributional uncertainties. The risk aversion and satisfaction degree affect the EIZ's strategy in wholesale market and retail market, respectively. © 2023 Institute of Electrical Engineer of Japan and Wiley Periodicals LLC. [ABSTRACT FROM AUTHOR]