Mining sequential rules from large databases is an important topic in data mining fields with wide applications. Most of the relevant studies focused on finding sequential rules appearing in a single sequence of events and the mining task dealing with multiple sequences were far less explored. In this paper, we present RuleGrowth, a novel algorithm for mining sequential rules common to several sequences. Unlike other algorithms, RuleGrowth uses a pattern-growth approach for discovering sequential rules such that it can be much more efficient and scalable. We present a comparison of RuleGrowth's performance with current algorithms for three public datasets. The experimental results show that RuleGrowth clearly outperforms current algorithms for all three datasets under low support and confidence threshold and has a much better scalability.