Sequential pattern mining is the mining of data sequences for frequent sequential patterns with time sequence, which has a wide application. Data streams are streams of data that arrive at high speed. Due to the limitation of memory capacity and the need of real-time mining, the results of mining need to be updated in real time. Multiple data streams are the simultaneous arrival of a plurality of data streams, for which a much larger amount of data needs to be processed. Due to the inapplicability of traditional sequential pattern mining techniques, sequential pattern mining in multiple data streams has become an important research issue. Previous research can only handle a single item at a time and hence is incapable of coping with the changing environment of multiple data streams. In this paper, therefore, we propose the IAspam algorithm that not only can handle a set of items at a time but also can incrementally mine across-streams sequential patterns. In the process, stream data are converted into bitmap representation for mining. Experimental results show that the IAspam algorithm is effective in execution time when processing large amounts of stream data.