Start-ups are important tools for promoting sustainable development through the creation of new ventures with a sustainable business model. However, to make a tangible contribution, start-ups need to embed and balance their sustainability impact in their business model from the very beginning. Incubators are a promising way to support them in this process. Despite the academic interest in incubators, few studies have focused on sustainable incubators in general, and even less on the sustainable business model development process. This study explores how a support programme delivered by an incubator with a sustainability profile can affect the sustainable business model development of start-ups. A case study approach based on a French incubator was used in combination with the resource-based view to understand the creation process of sustainability-oriented ventures and the resource needs of start-ups to achieve a sustainable impact. The results show that besides the classic support services for the development of a sustainable business model, there are additional interesting factors that come into play.