Sequence mining is an important data mining task. In order to retrieve interesting sequences from a large database, a minimum support threshold is needed to be specified. Unfortunately, specification of the appropriated support threshold is very difficult for users who are novice to mining queries and task specific data. To avoid this difficulty of specification of the appropriated support threshold, this paper is proposed to mine k most frequent closed sequences consisting of events containing a single item. This is called top-k closed sequences. This mining not only provides an easy way to retrieve interesting sequences but also gives the compact representation of sequences.