Sequential pattern mining under constraints is a challenging data mining task. Many efficient ad hoc methods have been developed for mining sequential patterns, but they are all suffering from a lack of genericity. Recent works have investigated Constraint Programming (CP) methods, but they are not still effective because of their encoding. In this paper, we propose a global constraint based on the projected databases principle which remedies to this drawback. Experiments show that our approach clearly outperforms CP approaches and competes well with ad hoc methods on large datasets.