Success in industrial construction project plays an important role in gaining the competitive advantage of the large-scale infrastructure enterprises. The present research proposes a hybrid fuzzy Multi-Criteria Decision-Making (MCDM) methodology to enhance the success in MAPNA Company, which is one of the largest contractors in the Middle Eastern oil industry. The new hybrid fuzzy MCDM framework is presented through the combination of fuzzy DEMATEL and fuzzy ANP methods and also extended to take into consideration the composite materials like Fiber-Reinforced Polymer (FRP), carbon fiber, and glass fiber. In accordance with the literature review, expert opinion, and Delphi technique from 10 experts, seven main criteria and 45 sub-criteria have been determined. Through the fuzzy DEMATEL method, the analysis of cause-effect relationship between the criteria has been conducted, and the results show that project management has the highest level of impact (D = 5.591), while project-related parameters are the most sensitive (R = 5.652). The threshold value of 0.737 has been considered to form Network Relation Map (NRM). Then, the fuzzy ANP method has been performed to prioritize the criteria. It was found that contractor related factors (normalized weight = 0.177) are the most important amongst main criteria, then project manager related factors (0.175), and finally project management (0.151). As far as the sub-criteria level is concerned, "construction regulations" (S8) has been awarded highest priority (weight = 0.0493) overall, while "customer influence" (S41 = 0.0378) and "certification of products and services" (S9 = 0.0368) were other highly prioritized criteria at this stage. In addition, composite-specific sub-criteria including material certification, specialized fabrication technology, supply chain assurance, and sustainability have also been incorporated in the extended model. FDANP framework offered as an innovative approach is quite reliable as a decision support system in dealing with complexities associated with uncertainties and interrelations in the context of industrial construction projects, especially those using composite materials.