Many clustering approaches have been developed for biological data analysis, however, the application of traditional clustering algorithms for RNA structure data analysis is still a challenging issue. This arises from the existence of complex secondary structures while clustering. One of the most critical issues of cluster analysis is the development of appropriate distance measures in high dimensional space. The traditional distance measures focus on scale issues, but ignores the correlation between two values. This article develops a novel interval-based distance (Hausdorff) measure for computing the similarity between characterized structures. Three relationships including perfect match, partially overlapped and non-overlapped are considered. Finally, we demonstrate the methods by analyzing a data set of RNA secondary structures from the Rfam database.