Aiming at the problems of strong coupling and weak anti-interference ability of the transition mode of the tilt-rotor UAV(unmanned aerial vehicle), a non-overshoot sliding mode control method was designed on the basis of simplifying the longitudinal dynamic model of the tilt-rotor UAV. It includes two bounded gain subsystems. The first subsystem realizes non-overshoot reachability, compresses the initial value to a given bounded range, and the second subsystem realizes local non-overshoot stability, so that the sliding variable converges to zero and there is no overshoot. Using the efficient global search ability of genetic algorithm, the gain parameters of sliding mode control and the boundary parameters of sliding mode variables in the non-overshoot sliding mode control method were optimized. The practicability and superiority of the method were verified by theoretical analysis and simulation experiments. The experimental results show that compared with the traditional synovial control, the designed non-overshoot synovial control method based on parameter optimization can achieve the expected value in a short time in terms of height control and pitch angle control. In the case of gust disturbance, the non-overshoot sliding mode controller shows better fluctuation suppression and amplitude control performance in height and pitch angle control. It effectively suppresses the occurrence of overshoot and chattering, improves the control accuracy, and shows stronger robustness and reliability.