Stream cube computing is the important foundation of data stream multidimensional analysis. But the features of data stream (dynamic, infinity, bursty, etc) and complexity of multidimensional data structure, are confronted with great challenges, such as storage space, updating efficiency, adaptability, and so on. In many applications, users often focus on only a portion of views. A computing method based on interesting view subset is proposed in this paper. Interesting view subset and interesting path can be obtained by the information of historical queries. And if the efficiency of answering queries decreases, it should be updated with the lapse of time. The Stream-Tree structure is defined for maintaining the cells of interesting view subset and drilling paths in memory. In the running phase, the cells of Stream-Tree are continuously updated with new tuple arriving, and the old cells are deleted periodically according to the constraints of multi-level time windows. The sparse cells of Stream-Tree will not be divided into finer ones, only the high level aggregations are preserved. Experiments and analysis results indicate that the method is efficient in maintaining the stream cube cells of current time window in finite memory, and can answer the queries of users quickly.