Hazardous waste management is of paramount importance due to the potential threats posed to the environment and local residents. The design of a hazardous waste management system involves several important decisions, i.e., the determination of the locations and sizes of treatment, recycling and disposal facilities, and organizing the transportation of hazardous waste among different facilities. In this paper, we proposed a novel stochastic bi-objective mixed integer linear program (MILP) to support these decisions in order to reduce the population exposure to risk while simultaneously maintaining a high cost efficiency of the transportation and treatment of hazardous waste. Moreover, considering the inherent uncertainty within the planning horizon, the cost, demand and affected population are defined as stochastic parameters. A sample average approximation based goal programming (SAA-GP) approach is used to solve the mathematical model. The proposed model and solution method are validated through numerical experiments whose results show that uncertainty may not only affect the objective value but also lead to different strategic decisions in the network design of a hazardous waste management system. In this regard, the strategic decisions obtained by the stochastic model is more robust to the change of external environment. Finally, the model is applied in a real-world case study of healthcare waste management in Wuhan, China, in order to show its applicability.