Purpose The study aims to identify Green Lean Six Sigma (GLSS) barriers in the context of Higher Education Institutions (HEIs) and prioritize them for executing the GLSS approach. Design/methodology/approach A systematic literature review (SLR) was used to identify a total of 14 barriers, which were then verified for greater relevance by the professional judgments of industrial personnel. Moreover, many removal measures strategies are also recommended in this study. Furthermore, this work also utilizes Gray Relational Analysis (GRA) to prioritize the identified GLSS barriers. Findings The study reveals that training and education, continuous assessment of SDG, organizational culture, resources and skills to facilitate implementation, and assessment of satisfaction and welfare of the employee are the most significant barriers to implementing this approach. Research limitations/implications The present study provides an impetus for practitioners and managers to embrace the GLSS strategy through a wide-ranging understanding and exploring these barriers. In this case, the outcomes of this research, and in particular the GRA technique presented by this work, can be used by managers and professionals to rank the GLSS barriers and take appropriate action to eliminate them. Practical implications The ranking of GLSS barriers gives top officials of HEIs a very clear view to effectively and efficiently implementing GLSS initiatives. The outcomes also show training and education, sustainable development goals and organizational culture as critical barriers. The findings of this study provide an impetus for managers, policymakers and consultants to embrace the GLSS strategy through a wide-ranging understanding and exploring these barriers. Social implications The GLSS barriers in HEIs may significantly affect the society. HEIs can lessen their environmental effect by using GLSS practices, which can support sustainability initiatives and foster social responsibility. Taking steps to reduce environmental effect can benefit society as a whole. GLSS techniques in HEIs can also result in increased operational effectiveness and cost savings, which can free up resources to be employed in other areas, like boosting student services and improving educational programs. However, failing to implement GLSS procedures in HEIs could have societal repercussions as well. As a result, it is critical for HEIs to identify and remove GLSS barriers in order to advance sustainability, social responsibility and operational effectiveness. Originality/value GLSS is a comprehensive methodology that facilitates the optimum utilization of resources, reduces waste and provides the pathway for sustainable development so, the novelty of this study stands in the inclusion of its barriers and HEIs to prioritize them for effective implementation.