Similarity search for data streams has attracted much attention for information recommendation. In this context, recent leading works regard the latest W items in a data stream as an evolving set and reduce similarity search for data streams to set similarity search. Whereas they consider standard sets composed of items, this paper uniquely studies similarity search for text streams and treats evolving sets whose elements are texts. Specifically, we formulate a new continuous range search problem named the CTS problem (Continuous similarity search for Text Sets). The task of the CTS problem is to find all the text streams from the database whose similarity to the query becomes larger than a threshold ε. It abstracts a scenario in which a user-based recommendation system searches similar users from social networking services. The CTS is important because it allows both the query and the database to change dynamically. We develop a fast pruning-based algorithm for the CTS. Moreover, we discuss how to speed up it with the inverted index.