Mining frequent patterns on biosequences is one of the important research fields in biological data mining. Traditional frequent pattern mining algorithms may generate large amount of short candidate patterns in the process of mining which cost more computational time and reduce the efficiency. In order to overcome such shortcoming of the traditional algorithms, we present an algorithm named MSPM for fast mining frequent patterns on biosequences. Based on the concept of primary patterns, the algorithm focuses on longer patterns for mining in order to avoid producing lots of short patterns. Meanwhile by using prefix tree of primary frequent patterns, the algorithm can extend the primary patterns and avoid plenty of irrelevant patterns. Experimental results show that MSPM can achieve mining results efficiently and improves the performance.