Of the current approaches to frequent pattern discovery in stream data, the batch approach requires enough data, while the heuristic approach can deal with stream data directly. Although the average speed of the batch approach is higher, it cannot response on time and the query granularity is rough. This paper proposes an improved Lexicographic tree, IL-TREE (improved lexicographic tree), and gives a novel heuristic algorithm, called FPIL-Stream (frequent pattern mining based on improved lexicographic tree), which locates the historical patterns rapidly in the stage of updating the patterns and generating the new ones. Moreover, a policy for the titled window is integrated into the algorithm for recording the historical information in details. With the promise of the processing stream data on time, the algorithm reduce the average processing time greatly and provides a finer granularity of query.