The sustainable supply chain network is mostly modeled based on the triple bottom line of economy, environment and society, which fails to fully describe the degree of correlation between the enterprise's own governance capability and the supply chain model. Meanwhile, to more accurately represent the real state of each uncertain parameter in the model, a fuzzy multi-objective sustainable supply chain network model was proposed based on CITI Evaluation Guide 8. 0, which modeled the quadruple bottom lines of economic cost, environmental pollution, social impact and corporate governance capability, and a hybrid metaheuristic algorithm named TSA-BB that combined taboo search and branch delimitation was designed to solve the model. The characteristics of each indicator of the quadruple bottom line were considered comprehensively, and the corresponding fuzzy hierarchical analysis structure model was established to represent the relative importance of each indicator. Then, the direct influence matrix and comprehensive influence matrix were constructed in turn according to the relative importance degree, and the weighted centrality of each indicator was calculated based on the two as the comprehensive weight of the integrated multi-objective function. Various algorithm rules were designed in TSA-BB to solve the model efficiently, and the feasibility and effectiveness of the model and algorithm were verified based on a large number of arithmetic simulations. The experimental results showed that the fuzzy indicators and quadruple bottom line co-modeling could better fit the real state of the supply chain, and the corporate governance capability should be an important decision basis for decision makers at all levels to consider in the balanced optimization of the supply chain network model. © 2024 CIMS. All rights reserved.