The FlexibleNeural Tree uses a tree structure coding and has excellent predictiveability and function approximation capabilities. Due to it, a quantum neural tree model ispresented based on the multi-level transfer function quantum neuralnetwork and Flexible Neural Tree. In the new model, based on the structure of FlexibleNeural Tree, the transfer function of hidden layer quantum neurons is insteadof multiple superposition oftraditional transfer function, makes the model has a kind of inherent ambiguity.This paper used the improved neural tree asprediction model, particle swarm optimization to optimize the parameters of neuraltree, used probabilistic incremental program evolution to optimizethe structure of neural tree. The experiment result for stock index predictionshows the now method can improve the predictive accuracy rate