Commonly-known for their sophisticated and robust results, and some lack of time-to-market orientation, the universities are reviewing their roles to be more competitive in the innovation ecosystems. The actual context is large growing of acceleration programs to promote Open Innovation in startups, as well as traditional corporations, interested in the development of innovation across organisational boundaries. Although recent studies emphasise that startups developed or supported by universities have more expectations of success than non-academic startups, the movement of acceleration programs with an emphasis on open innovation is not always connected to universities and supported for research and development. This fact indicates that there are opportunities to encourage the work of universities with companies and other actors for the development of market-oriented proposals and innovative solutions that cover different fields of knowledge through transdisciplinary research. This study has as main objective to identify practices and impacts of acceleration programs for open innovation and its relationship with Research and Development in universities. This study is conducted in two phases in order to analyse the impacts: the first is a systematic review of the literature to identify state of the art of the studied themes in a combined manner. The second phase of the article consists in study two application cases of acceleration programs at the Pontifical Catholic University of Paraná. The work aims to analyse the impacts of the open innovation and acceleration programs found in the literature and in the case study in order to identify opportunities for improvement for the programs of acceleration of open innovation which universities propose or participate. The expected result is to provide subsidies for universities to increase their participation and contribution in programs, to accelerate innovation and open innovation, supported by transdisciplinary and excellent research.