In view of the issue of transition thrust pinch during power transitions in hybrid propulsion aircraft, a switching control method is proposed for hybrid propulsion aircraft considering thrust pinch.Firstly, for the normal flight control requirements of hybrid propulsion aircraft, a normal flight controller is designed by using a sliding mode control approach based on the super-twisting algorithm, enabling the aircraft to achieve finite-time stable tracking of reference commands in the presence of disturbances. Secondly, in consideration of the control constraints imposed by thrust losses during power transitions, an input-constrained controller is designed to facilitate limited-time convergence of tracking errors during the mode transition phase while reducing the demand for thrust. Furthermore, in combination with the controllers for a normal flight or on a mode transition phase, a soft switching control strategy for combined engine transitions is designed. Finally, the simulation experiments show that the designed controller can not only effectively avoid thrust loss phenomenon, and effectively ensure the stability and the robustness in the switching control system.