RNA secondary structures with pseudoknots are often predicted by minimizing free energy, which is NP-hard. Most RNAs fold during transcription from DNA into RNA through a hierarchical pathway wherein secondary structures form prior to tertiary structures. Real RNA secondary structures often have local instead of global optimization because of kinetic reasons. The performance of RNA structure prediction may be improved by considering dynamic and hierarchical folding mechanisms. This study is a novel report on RNA folding that accords with the golden mean characteristic based on the statistical analysis of the real RNA secondary structures of all 480 sequences from RNA STRAND, which are validated by NMR or X-ray. The length ratios of domains in these sequences are approximately 0.382L, 0.5L, 0.618L, and L, where L is the sequence length. These points are just the important golden sections of sequence. With this characteristic, an algorithm is designed to predict RNA hierarchical structures and simulate RNA folding by dynamically folding RNA structures according to the above golden section points. The sensitivity and number of predicted pseudoknots of our algorithm are better than those of the Mfold, HotKnots, McQfold, ProbKnot, and Lhw-Zhu algorithms. Experimental results reflect the folding rules of RNA from a new angle that is close to natural folding.