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Existing literature ignores to consider multiple types of pollutants when analyzing energy efficiency and its convergence. Under this background, using SuperSBM-GML model, the improved entropy method, and convergence model, this paper calculates the green total-factor energy efficiency and its evolution trend of 35 China's industrial sub-sectors considering multiple pollutants, and analyzes its convergence. The results indicate that the average score of industrial green total-factor energy efficiency is low, and there are significant differences among sub-sectors: "Utilization of waste resources" is the highest, while "Manufacture of paper and paper products" is the lowest. The green total-factor energy efficiency shows an overall upward trend from 2006 to 2021, the main driving force comes from technological progress, but numerous sub-sectors have not sufficiently caught up with existing cutting-edge technologies. Specifically, the growth rate of green total-factor energy efficiency in high-energy-consumption sub-sectors is higher than low-to-medium-energy-consumption sub-sectors. There are both σ-convergence and β-convergence in low-to-medium-energy-consumption group, indicating that development of sub-sectors is stable and outstanding. Nevertheless, the high-energy-consumption group only exhibits conditional β-convergence, revealing an imbalance in energy efficiency development. Consequently, formulating the benchmark level of energy efficiency and developing energy efficiency "leader" system are suggested for low-to-medium and high-energy-consumption sub-sectors, respectively. [ABSTRACT FROM AUTHOR]