Sequential pattern mining is an important problem in continuous, fast, dynamic and unlimited stream mining. Recently approximate mining algorithms are proposed which spend too many system resources and can only obtain the partial feature of stream. In this paper, a multi-level evolving sequential pattern mining model ESPMM is presented to address this problem thus the mostly entire stream feature is obtained. Furthermore, because of the smaller support of sequential patterns in each level, a mining method BMLA based on Levenshtein-Automata is proposed which builds state conversion model to compute sequences' similarity in linear time. The experiment results show this model is effective and efficient.