Distributed energy sharing is an important means for enterprises to improve energy efficiency and reduce carbon emissions. However, the uncertainty of benefits under the carbon tax policy triggers the disappointment aversion behavior of decision makers, which has an important impact on the energy sharing decision of industrial clusters. This paper adopts the differential game approach to study the dynamic coordination problem of distributed energy sharing in industrial clusters, explores the optimal equilibrium strategies under different decision-making models, analyzes the impacts of carbon tax rate and disappointment aversion behavior on decision-making, and finally conducts numerical simulations. The results show that the equilibrium results of centralized decision-making are better than those of decentralized decision-making, and the cost-sharing contract can achieve the coordination of decentralized decision-making. The higher the degree of disappointment aversion of industrial cluster members, the lower the motivation of energy sharing. Increasing the carbon tax rate is conducive to improving the energy low carbon level and energy sharing synergy effect of enterprises. However, when the initial carbon emissions of enterprises are high, it will lead to a decline in their profits. Therefore, the government should choose an appropriate carbon tax rate according to the initial carbon emissions of enterprises.