The COVID-19 pandemic has implications for the container shipping industry and global supply chains. Measuring the efficiency of major international container shipping companies (CSCs) is an important issue that helps them make strategic decisions to improve performance, especially in the context that all businesses and governments are adapting to build back better the post-pandemic world. This paper develops a new integrated approach using both a qualitative assessment tool and a performance assessment tool as a systematic and flexible framework for evaluating the container shipping industry. This new methodology is implemented in two phases to consider both qualitative and quantitative criteria for assessing the performance of CSCs based on efficiency. In the first phase, qualitative performance evaluation is performed using spherical fuzzy analytical hierarchical process (AHP-SF) to find criteria weights and then the grey complex proportional assessment methodology (COPRAS-G) is used to find the ranking of CSCs. Qualitative variables are converted into a quantitative variable for use in the data envelopment analysis (DEA) model as an output called an output variable called expert-based qualitative performance (EQP). Then, DEA is performed to identify efficient and inefficient CSCs with the EQP variable and other quantitative parameters (i.e., capacity, lifting, expenses, revenue, and CO2 emissions). The efficiency of 14 major global CSCs is empirically evaluated, and the scores for CSCs’ efficiency in all dimensions are measured and examined. The results show that the average cargo efficiency of the CSCs is lower than their eco-efficiency performance, revealing the operational disruption caused by the pandemic. Moreover, by identifying efficient and inefficient CSCs, our findings provide practical implications for decision-makers in the maritime field and assist in modifying applicable policies and strategies to achieve sustainable performance.