Due to the proliferation of the Internet and intranet, new application domains such as stream data processing have emerged. Stream data is real-timely and continuously generated. In stream data environments, a lot of queries are registered, and then, the arrived data item is evaluated by registered queries. Thus, to accelerate the query performance, diverse continuous query index schemes have been proposed for stream data processing systems. In this paper, we focus on the query index technique for stream data. In general, a stream query contains the range condition. Thus, by using range conditions, the queries can be indexed. In this paper, we propose an efficient query index scheme, called QUISIS, using a modified Interval Skip Lists to accelerate search time. QUISIS utilizes a locality where a value which will arrive in near future is similar to the current value. Through the experimental study, we show the efficiency of our proposed method.