Abstract: Sequential mining methods efficiently discover all frequent sequential patterns included in sequential data. These methods use the support, which is the previous criterion that satisfies the Apriori property, to evaluate the frequency. However, the discovered patterns do not always correspond to the interests of analysts, because the patterns are common and the analysts cannot get new knowledge from the patterns. The paper proposes a new criterion, namely, the sequential interestingness, to discover sequential patterns that are more attractive for the analysts. The paper shows that the criterion satisfies the Apriori property and how the criterion is related to the support. Also, the paper proposes an efficient sequential mining method based on the proposed criterion. Lastly, the paper shows the effectiveness of the proposed method by applying the method to two kinds of sequential data.