In this research, we aim to provide a tree similarity algorithm for RNA (ribonucleic acid) secondary structure comparison. The elements (nucleotides and nucleotide-pairs) of an RNA secondary structure are represented as normalized node-weighted trees. We show that our weighted tree representations of RNA secondary structures are more informative and useful. Based on this unique representation for RNA secondary structure, we propose a weighted-tree similarity algorithm for computing the similarity between RNA secondary structures. The algorithm is justified by computing similarities among several well-known RNA secondary structures. For a given RNA secondary structure, the proposed algorithm provides a ranked list of RNA structures in a database according to their similarity values with the query RNA. Hence, our algorithm can be helpful in predicting the functions and the class of a newly discovered RNA.