A robust positively invariant(RPI) set is designed for the trajectory tracking problem of a multi-rotor unmanned aerial vehicles(UAVs) subject to external disturbance and input saturation. With considering the nonlinear dynamics, external disturbance and input saturation of the multi-rotor UAV, a nonlinear control law with disturbance offset is designed firstly to ensure the stability of tracking, and the RPI set is constructed based on linear matrix inequalities(LMIs). For the tracking error within the designed RPI set, the designed control law can always guarantee that the tracking error stays in the RPI set forever and eventually converges to zero. The above properties are verified by the theoretical derivation and simulation results.