With the development of new technologies in transcriptome and epigenetics, RNAs have been identified to play more and more important roles in life processes. Consequently, various methods have been proposed to assess the biological functions of RNAs and thus classify them functionally, among which comparative study of RNA structures is perhaps the most important one. To measure the structural similarity of RNAs and classify them, we propose a novel three dimensional (3D) graphical representation of RNA secondary structure, in which an RNA secondary structure is first transformed into a characteristic sequence based on chemical property of nucleic acids; a dynamic 3D graph is then constructed for the characteristic sequence; and lastly a numerical characterization of the 3D graph is used to represent the RNA secondary structure. We tested our algorithm on three datasets: (1) Dataset I consisting of nine RNA secondary structures of viruses, (2) Dataset II consisting of complex RNA secondary structures including pseudo-knots, and (3) Dataset III consisting of 18 non-coding RNA families. We also compare our method with other nine existing methods using Dataset II and III. The results demonstrate that our method is better than other methods in similarity measurement and classification of RNA secondary structures.