Purpose Numerous and diverse organizations have implemented lean principles and practices, which concentrate on improving the efficiency of business processes by reducing cost, waste, consumptions and effort. However, previous assessments have not focused on the leanness of the supply chain in a health-care setting. This paper aims to introduce a method for assessing the successful implementation of lean principles and tools in a supply chain. Furthermore, this paper validates the method in a health-care organization. Design/methodology/approach This paper starts with an extensive literature review on assessing leanness and using multi-grade fuzzy logic. Then, a conceptual model was developed to measure leanness. The conceptual model was validated by discussing the initial version with select academic experts, especially those who deal with leanness in health-care organizations. After responding to the experts’ valuable comments, the health-care organization that is the focus of this case study was chosen based on two criteria. The first criterion was the organization’s ability to participate in the study, and the second was the organization’s commitment to implementing lean principles. These criteria were important to ensure the organization had the necessary foundation for implementing change initiatives such as lean process improvements. Next, a multi-grade (multi-attributes) fuzzy logic was used for leanness measurement. A leanness index was calculated, and the results were validated using experts from the case study organization. Finally, the weaker areas of the organization’s processes were identified to point the way for further improvements. Findings The assessment indicated that the case study organization is not lean. The organization’s weaker attributes were identified, and improvements have been suggested. Research limitations/implications This study focused on a single health-care organization, which was selected from a limited pool of potential organizations, namely, organizations which are accredited by both the Saudi Central Board for Accreditation of Healthcare Institutions and the Joint Commission International. The scope of future research should be extended to multi-case studies to enhance the findings presented in this paper. This paper’s findings can be used to help decision-makers at health-care providers to implement lean thinking in supply chain processes. Practical implications This research may be interest to practicing supply chain managers, as it proposes what enablers, factors and attributes should be emphasized in lean implementation. The proposed model can work as an assessment tool to identify the gap between the present level of leanness and the desired leanness state so the health-care organization can identify what can be improved. This model enables decision-makers in hospital supply chain to take suitable actions for improving lean implementation level. Originality/value This study makes an original contribution to the body of research concerning lean principles; the study developed a conceptual model for leanness assessment that can be applied to the supply chain of health-care organizations. Indeed, the conceptual model is likely to be useful for assessing leanness outside of the health-care field, which suggests avenues for future research.