Abstract：ABSTRACT：A new hybrid quantum particle swarm (QPSO) and Broyden quasi-Newton algorithm was put forward to reduce the dependence on the initial value and improve the convergence and the efficiency of the algorithm in solving the Variable Cycle Engine(VCE) model. Based on the analysis of the variable geometry characteristics of VCE, and the analysis of the steady state of external duct with BP Neural Network, a full envelop VCE model was established which can reflect the variation of variable geometry components. The new hybrid algorithm was used to solving the VCE model cooperating equations, which improved the dependence of single Broyden quasi-Newton method on the initial value and improved the efficiency of the hybrid algorithm by introducing the divergence coefficient. The efficiency and accuracy of the algorithm was verified by the simulation of high-order nonlinear equations. Finally, the results of VCE model show that the new hybrid algorithm can quickly complete the performance calculation of VCE component model. In addition, compared with the results of Gasturb performance calculation, it can be seen that the variation trend of velocity characteristics and altitude characteristics of VCE model are basically consistent with Gasturb and the error is less than 2%. The Broyden quasi - Newton hybrid algorithm based on quantum particle swarm optimization can solve the VCE model efficiently and quickly. The VCE model can effectively realize the performance simulation and analysis of this new engine.