Frequent sequence mining is an important data mining task with broad applications. To mine frequent sequences, a minimum support threshold is required as a filter. If a very small support threshold value is given in the mining process, a large number of resulting sequences may be produced. Consequently, users have to find useful sequences from the large number of resulting sequences and make tasks of analyze complicated. To avoid this problem, the most frequent sequences should be mined instead of mining of all frequent sequences because they are always the useful sequences. Therefore, this paper is proposed to mine the most frequent sequences. Moreover, the most frequent sequences are produced in form of closed sequences, called the most frequent closed sequences, to avoid generation of redundant sequences. In addition, an efficient method is presented in this paper for mining the most frequent closed sequences.