Previous studies on frequent pattern discovery from temporal sequence mainly consider finding global patterns, where every record in a sequence contributes to support the patterns. In this paper, we present a novel problem class that is the discovery of local sequential patterns, which only a subsequence of the original sequence exhibits. The problem has a two-dimensional solution space consisting of patterns and temporal features, therefore it is impractical that use traditional methods on this problem directly in terms of either time complexity or result validity. Our approach is to maintain a suffix-tree-like index to support efficiently locating and counting of local patterns. Based on the index, a method is proposed for discovering such patterns. We have analyzed the behavior of the problem and evaluated the performance of our algorithm on both synthetic and real data. The results correspond with the definition of our problem and verify the superiority of our method.