Sequential pattern mining is to find out all the frequent sub-sequences in a sequence database. In order to have more accurate results, constraints in addition to the support threshold need to be specified in the mining. Time-constraints cannot be managed by retrieving patterns because the support computation of patterns must validate the time attributes for every data sequence in the mining process. In this paper, we propose a memory time-indexing approach (called METISP) to discover sequential patterns with time constraints including minimum/maximum/exact gaps, sliding window, and duration. METISP scans the database into memory and constructs time-index sets for effective processing. Utilizing the index sets and the pattern-growth strategy, METISP efficiently mines the desired patterns without generating any candidate or sub-database. The comprehensive experiments show that METISP outperforms GSP and DELISP in the discovery of time-constrained sequential patterns, even with low support thresholds and very large databases.