Considering the uncertain parameters in the model of the trajectory tracking and controlling of quad-rotor aircrafts, an adaptive control algorithm is proposed based on the contraction theory and the backstepping method.Firstly, the contraction theory based on differential geometry is introduced, and the dynamic model of the quad-rotor aircraft is given.Then, the adaptive contraction backstepping control method is proposed for tracking the desired trajectory of the aircraft.Finally, the incremental stability of the system is analyzed, and it is proved that the error of the system is converged.The simulation results of Integral Backstepping (IB) and Adaptive Contraction Backstepping (ACB) show that, the aircraft system using the proposed control algorithm has higher robustness, and can implement trajectory tracking more accurately.