Due to the development of web technologies and the increasing use of smart devices such as smart phone, in recent various web services are widely used in many application fields. In this environment, the topic of supporting personalized and intelligent web services have been actively researched, and an analysis technique on a web-click stream generated from web usage logs is one of the essential techniques related to the topic. In this paper, for efficient analyzing a web-click stream of sequences, a sequential pattern mining technique is proposed, which satisfies the basic requirements for data stream processing and finds a refined mining result. For this purpose, a concept of interesting sequential patterns with a time-interval constraint is defined, which uses not on1y the order of items in a sequential pattern but also their generation times. In addition, A mining method to find the interesting sequential patterns efficiently over a data stream such as a web-click stream is proposed. The proposed method can be effectively used to various computing application fields such as E-commerce, bio-informatics, and USN environments, which generate data as a form of data streams.