In the process of long-distance and large-volume transportation of hazardous materials (HAZMAT), multimodal trans-portation plays a crucial role with its unique advantages. In order to effectively reduce the transportation risk and improve the reliability of transportation, it is particularly important to choose a suitable transportation plan for multimodal transport of HAZMAT. In this paper, we study the transportation of HAZMAT in multimodal transport networks. Considering the fluctuation in demand for HAZMAT during the actual transportation process, it is difficult for decision makers to obtain the accurate demand for HAZMAT orders in advance, leading to uncertainty in the final transportation plan. Therefore, in this paper, the uncertain demand of HAZMAT is set as a triangular fuzzy random number, and a multi-objective mixed integer linear programming model is established with the objective of minimizing the total risk exposure population and the total cost in the transportation process of HAZMAT. In order to facilitate the solution of the model, we combined the fuzzy random expected value method with the fuzzy random chance constraint method based on credibility measures to reconstruct the uncertain model clearly and equivalently, and designed a non-dominated sorting genetic algorithm (NSGA-) to obtain the Pareto boundary of the multi-objective optimization problem. Finally, we conducted a numerical example experiment to verify the rationality of the model proposed in this paper. The experimental results indicate that uncertain demand can affect the path decision-making of multimodal transportation of HAZMAT. In addition, the confidence level of fuzzy random opportunity constraints will have an impact on the risk and economic objectives of optimizing the multimodal transportation path of HAZMAT. When the confidence level is higher than 0.7, it will lead to a significant increase in transportation risks and costs. Through sensitivity analysis, it can provide useful decision-making references for relevant departments to formulate HAZMAT transportation plans.