Conventional sequential pattern mining methods may meet inherent difficulties in mining databases with long sequences and noise. They may generate a huge number of short and trivial patterns but fail to find interesting patterns approximately shared by many sequences. In this paper, we propose the theme of approximate sequential pattern mining roughly defined as identifying patterns approximately shared by many sequences. We present an efficient and effective algorithm, ApproxMAP, to mine consensus patterns from large sequence databases in two steps. First, sequences are clustered by similarity. Then, consensus patterns are mined directly from each cluster through multiple alignment. We use a real case study to illustrate the effectiveness of ApproxMAP.