This study presents a decision making tool for risk management of a carbon capture utilization and storage (CCUS) network under uncertainty among conflicting objectives. A two-phase-two-stage stochastic multi-objective optimization problem solving algorithm is formulated to balance environmental impact and various sources of uncertainty and corresponding risk by installing and operating a CCUS network. The algorithm allows decision makers to choose their own tolerance on risk. By conducting case studies that have different target profits for CCUS networks, the algorithm provides optimal results based on the decision maker's attitude to risk. To evaluate risks imposed by uncertain parameters, a concept of downside risk is introduced. By setting different target profit levels, the suggested tool enables decision makers to choose their own tolerance and preference for risk. In the model, the life cycle assessment is applied to evaluate all environmental contributions caused by installation and operations of the CCUS network. The model provides the trade-off relationship between total annual benefit with financial risk as well as corresponding environmental impact. The aim of this model to optimize CCUS supply chain networks is to provide an intuitive decision making algorithm to balance conflicting objectives within a single framework. This problem is formulated as a mixed integer linear program model. To illustrate the applicability of the model, four optimal CCUS network models for the various types of industrial complex of Korea in 2030 are presented. Results indicate that risk-averse cases with a low profit target are more reliable in stochastic uncertainty, and that risk-taking decision makers tend to invest more on capture facility and produce more product than do, risk-averse decision makers.