Purpose Increasing pressure from the stakeholders makes the inclusion and evaluation of sustainable practices in the service supply chain (SSC) inevitable. Therefore, this paper aims to evaluate the sustainability status of a case organization and discover the barrier to sustainability in the SSC. Design/methodology/approach From the literature review, five sustainability dimensions, seventeen attributes and sixty-five subattributes of the SSC are identified. A three-level conceptual model drawn on human perception is developed. The overall sustainability status of the SSC is determined by using the multigrade fuzzy logic approach. The fuzzy concept incorporated helps in overcoming the challenges of vagueness and impreciseness in the responses. The case SSC is a WestIndia-based hospital. Findings The study evaluates the case hospital to be "very sustainable" but far from the "extremely sustainable" level. Six barriers are identified which are reduction in solid waste, compliance with applicable environmental laws and regulations, water usage efficiency, training and education of employees, return on investment and safety equipment for employees. These barriers hinder the hospital from achieving an "extremely sustainable" level. Practical implications This paper evaluates, helps the management in identifying the barriers and thus enabling them to work upon these barriers and achieve a greater level of sustainability. Originality/value The sustainability practices adopted in this paper for the evaluation of the sustainability status of the SSC have not been used in previous studies. In this study apart from environmental, social and economic aspects, customer management and health, safety and risk management are also incorporated for evaluating the performance of the SSC which makes this study unique. The proposed model can be taken as a benchmark for evaluating the sustainability performance of any SSC.