An input constrained adaptive tracking controller is designed for flapping micro aerial vehicles, wherein the moving averaging filter is adopted to estimate the averaged states of the system. Specifically, in the outer loop controller, an observer is constructed to estimate the disturbances within the system. Moreover, the constrained thrust is designed to keep the frequency in a proper region so as to meet the requirement of average estimation. Then, a tracking differentiator is used to provide trackable trajectories for the inner loop. Subsequently, a new quaternion-based hybrid attitude tracking controller is designed which successfully deals with high-frequency noises and avoids possible chattering. As supported by mathematical analysis, the proposed control strategy guarantees the uniform ultimate boundedness of the closed-loop system, and it keeps the control torques within the permitted range to meet the application requirement. At last, numerical simulations are carried out to support the validity of the proposed controller, whose results are satisfactory even when the thrust and torques are saturated.