Based on the circuit structure of Buck-Boost converter, the Lagrange function of the system is obtained using the energy method, and the dynamic equations of BuckBoost converter are established. The infinitesimal transformations of time and charge generalized coordinates are introduced, and based on the invariance of the Hamiltonian action of the system,Noether identity, generalized Killing equation, and generalized Noether theorem of BuckBoost converter are given. The symmetries of Buck-Boost converter in the on or off state are studied, and the corresponding conservation quantities are obtained. Based on this, the exact solutions of dynamic equations for the converter are constructed, and the results are applied to the time response analysis of BuckBoost converter. Through experiments, the time responses calculated using the Noether symmetry method and the Runge-Kutta fourthfifth order method (ode45) are compared. The results indicate that the Noether symmetry method not only maintains high accuracy but also significantly enhances the calculation speed of the system's time response.