The study of protein tertiary structure prediction is useful to protein function. This paper proposes a novel protein tertiary structural prediction approach based on flexible neural tree (FNT). In this approach, the approximate entropy and hydrophobicity pattern of a protein sequence are adopted to characterize the Pseudo-Amino Acid (PseAA) components as input. A novel quantum particle swarm optimization (QPSO) combined with the speed and disturbance is presented and used to optimize the parameters of FNT. The 640 protein sequence is used as the dataset. The experiment data is validated by ten- fold cross validation and the result shows the approach based on the novel quantum particle swarm optimization and FNT can improve the predictive accuracy.