Sequential pattern mining, which discovers frequent subsequences as patterns in a sequence database, in an important data-mining problem with broad applications. Although conventional sequential patterns can reveal the order of items, the time between items is not determined; that is, a sequential pattern does not include time intervals between successive items. Accordingly, this work addresses sequential patterns that include time intervals, called time-interval sequential patterns. This work develops two efficient algorithms for mining time-interval sequential patterns. The first algorithm is based on the conventional Apriori algorithm, while the second one is based on the PrefixSpan algorithm. The latter algorithm outperforms the former, not only in computing time but also in scalability with respect to various parameters.