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Purpose: Carbon capture and storage (CCS) has been well recognized as an effective approach to reducing CO2 emissions, but the emergence of various CCS technologies has resulted in the challenge of selecting the most sustainable alternative. This study aims to develop a mathematical framework to evaluate the sustainability of different CCS technologies determe the best-performing one and identify the key affecting criteria. Methods: The mathematical framework was developed by combining the multi-criteria decision-making (MCDM) approach with the life cycle assessment (LCA), which can overcome the difficulty to obtain the criteria data, especially for the environmental aspect. A novel weighting method of grey correlation weighting (GCW), which is more applicable to the criteria data obtained by LCA, is presented for objectively weighting the criteria and identifying key criteria with the consideration of criteria interaction. The sustainability of different CCS technologies is ranked by using the method of similarity to the ideal solution (TOPSIS). The effectiveness of the developed mathematical framework is verified by a case study with 9 different CCS technologies. Results: The results show that the CCS process with the pre-combustion capture technology by using CaO as the absorbent is the most sustainable one. For both pre-combustion and post-combustion capture technologies, it is critical to improve their environmental performance for enhancing their sustainability, while for increasing the sustainability of the oxyfuel combustion technology, the key is to reduce the "capital cost". The validity of the developed framework was demonstrated through sensitivity analysis and comparison with conventional MCDM methods. Conclusions: The developed LCA-MCDM methodology is effective to assess the sustainability of various CCS technologies. The results of the sustainability evaluation using the methodology demonstrated that the environmental performance of the CCS technologies has the largest impact on sustainability, while if the cost of the air separation process can be addressed, the sustainability of oxyfuel combustion technologies can be greatly improved. [ABSTRACT FROM AUTHOR]