This contribution explores the role of Corporate Social Responsibility (CSR) on the adoption on Sustainability Oriented Innovation. In accordance with previous research that show the effect of CSR depends on which CSR practices are taking into account, we consider different measures of CSR practices To analyse this relationship we adopt an empirical approach based on a survey carried on in Luxembourg in 2008 on firm CSR practices jointly with the Community Innovation Survey carried on in 2012. With a sample of 286 firms and a Heckman procedure, the study underlines the importance to differentiate the type of CSR strategy (strategic vs responsive). Our results show that strategic CSR explain the adoption of Sustainability Oriented Innovation.