There are some NP-hard problems in the prediction of RNA structures. Prediction of RNA folding structure in RNA nucleotide sequence remains an unsolved challenge. We investigate the computing algorithm in RNA folding structural prediction based on extended structure and basin hopping graph, it is a computing mode of basin hopping graph in RNA folding structural prediction including pseudoknots. This study presents the predicting algorithm based on extended structure, it also proposes an improved computing algorithm based on barrier tree and basin hopping graph, which are the attractive approaches in RNA folding structural prediction. Many experiments have been implemented in Rfam14.1 database and PseudoBase database, the experimental results show that our two algorithms are efficient and accurate than the other existing algorithms.