Abstract: The convergence problems of solving the nonlinear equations of aero turbo-engines were studied in detail,while the non-convergence cases were counted and the mechanism was analyzed.For solving the common non-convergence problems,some improved methods based on Newton method were presented,such as: limitation of initial variables of the nonlinear equations based on components maps,polynomial fit of initial values of variables of the nonlinear equations,variable step Newton method and expansion of components' maps.These improved methods were employed in performance computing program.The performance calculation results of some fix geometry turbojet and variable geometry turbofan show that the convergence and convergence rate have been improved greatly.