In several applications, sequence databases generally update incrementally with time. Obviously, it is impractical and inefficient to re-mine sequential patterns from scratch every time a number of new sequences are added into the database. Some recent studies have focused on mining sequential patterns in an incremental manner; however, most of them only considered patterns extracted from time point-based data. In this paper, we proposed an efficient algorithm, Inc-TPMiner, to incrementally mine sequential patterns from interval-based data. We also employ some optimization techniques to reduce the search space effectively. The experimental results indicate that Inc-TPMiner is efficient in execution time and possesses scalability. Finally, we show the practicability of incremental mining of interval-based sequential patterns on real datasets.