Sequential pattern mining is a popular data mining task with wide applications. However, it may present too many sequential patterns to users, which makes it difficult for users to comprehend the results. As a solution, it was proposed to mine maximal sequential patterns, a compact representation of the set of sequential patterns, which is often several orders of magnitude smaller than the set of all sequential patterns. However, the task of mining maximal patterns remains computationally expensive. To address this problem, we introduce a vertical mining algorithm named VMSP (Vertical mining of Maximal Sequential Patterns). It is to our knowledge the first vertical mining algorithm for mining maximal sequential patterns. An experimental study on five real datasets shows that VMSP is up to two orders of magnitude faster than the current state-of-the-art algorithm.