A nonlinear mixed integer programming model was established with the optimization objective of minimizing closed-loop supply chain operation cost and maintenance cost with considering the complexity of network structure, aiming at the closed-loop network design problems under the uncertainty of customer demand and the failure of some facility nodes. The robust counterpart theory and the scenario analysis of robust optimization were used to deal with the demand uncertainty and the interruption uncertainty of a single facility node. The information entropy theory was used to quantify the network structure complexity and a piecewise linearization was used to make linear construction of structural complexity. A robust optimization model under the influence of mixed uncertainties was constructed. The Gurobi solver was used to make node opening or not and traffic allocation decisions. The case study shows that, when considering the network structure complexity, the fluctuation amplitude of the objective function value of robust optimization model under uncertain scenarios is significantly reduced compared with that of the stochastic programming model, and it is proved that the established model has a good ability to resist external risks.