Sustainability-oriented start-ups are fundamental to developing solutions for, and to fostering, a societal transition towards a low carbon society. In this context, social impact accelerators (SIAs) are organizations specializing in accelerating the progress of sustainability-oriented start-ups. In order to design their accelerator elements (e.g., training, coaching, and funding) effectively, SIAs must be aware of the knowledge needs of start-ups to support them in developing a sustainable business model (SBM). Using a case study approach, we present one of the largest cleantech accelerator programs in Europe, the EIT Climate-KIC RIS Accelerator. Based on the program’s curriculum and manual in 2019, we analyze from the perspective of the program how cleantech start-ups could be supported in the development of their SBMs by presenting accelerator elements that are intended to support start-ups in reducing their knowledge needs by (1) providing new knowledge to start-ups (e.g., trainings, workshops, and e-learning), (2) supporting start-ups’ assimilation of new knowledge (e.g., coaching), and (3) supporting start-ups’ application of new knowledge (e.g., documentation of planning and reporting as part of the program’s contract design). Further, we discuss the knowledge needs of 63 European start-ups before and their progress as a result of accelerator participation in developing a SBM based on qualitative and quantitative data. All 63 start-ups participated in the same batch of the accelerator in 2019. Regarding the development of a SBM, knowledge needs are described considering the triple bottom line including the economic, ecological, and social layer of a business model. Based on the start-ups’ evaluation, we reflect—with a focus on the environmental layer—about the most promising content and support elements of our SIA case to address the different layers, discuss their combination, and present improvement potentials to reduce start-ups’ knowledge needs. With our findings, we claim to contribute to theory development in the emerging literature on SIAs and give practitioners working with sustainability-oriented start-ups insights into the usefulness of start-up support programs and different accelerator elements for developing a SBM.