In order to prepare Rwandan citizens for a competitive world, a competence-based curriculum (CBC) has been implemented since 2016. The problem addressed by this study is "under which conditions will the implementation of the intended science curriculum be realised in classroom". Framed by the Rogan and Grayson theory of curriculum implementation, a multiple case study was conducted to explore the relationships between a school's profile of science CBC implementation and its capacity to support innovation. This was done by interviewing 12 teachers, observing and recording 23 of their science lessons, and surveying school facilities in their three schools. The data were presented in narrative form based on ratings (1-4) of lessons and schools' capacity to innovate. Despite the variations between teachers and schools in CBC implementation caused by differences in individual professional development and schools' capacity to innovate, the results revealed high levels of appropriate CBC implementation in aspects of classroom interactions, teaching and learning activities, and assessment. On the other hand, a low implementation level was noticed in the aspect of science-in-society. The study findings relate the profile of science CBC implementation to some aspects of a school's capacity to innovate, particularly individual teacher's experience, inadequate preparedness to enact CBC and inadequate teaching and learning resources for science. For successful implementation of science CBC, strong and regular training programmes that focus on how the new ideas are put into practice, together with the provision of teaching and learning resources for science, are recommended.