Sequence pattern mining is an important research problem because it is the basis of many other applications. Yet how to efficiently implement the mining is difficult due to the inherent characteristic of the problem - the large size of the data set. In this paper, by combining SPAM, we propose a new algorithm called LAst Position INduction Sequential PAttern Mining (abbreviated as LAPIN-SPAM), which can efficiently get all the frequent sequential patterns from a large database. The main difference between our strategy and the previous works is that when judging whether a sequence is a pattern or not, they use S-Matrix by scanning projected database (PrefixSpan) or count the number by joining (SPADE) or ANDing with the candidate item (SPAM). In contrast, LAPIN-SPAM can easily implement this process based on the following fact - if an item?s last position is smaller than the current prefix position, the item can not appear behind the current prefix in the same customer sequence. LAPIN-SPAM could largely reduce the search space during mining process and is considerable effectiveness in mining sequential pattern. Our experimental results show that LAPIN-SPAM outperforms SPAM up to three times on all kinds of dataset.