Sequential pattern mining has been studied extensively in data mining community. Most previous studies require the specification of a minimum support threshold to perform the mining. However, it is difficult for users to provide an appropriate threshold in practice. To overcome this difficulty, we propose an alternative task: mining top-k frequent closed sequential patterns of length no less than min-ℓ, where k is the desired number of closed sequential patterns to be mined, and min-ℓ is the minimum length of each pattern. We mine closed patterns since they are compact representations of frequent patterns. We developed an efficient algorithm, called TSP, which makes use of the length constraint and the properties of top-k closed sequential patterns to perform dynamic support-raising and projected database-pruning. Our extensive performance study shows that TSP outperforms the closed sequential pattern mining algorithm even when the latter is running with the best tuned minimum support threshold.