This paper studies an adaptive dynamic programming (ADP) based finite-horizon robust optimal trajectory tracking control problem for quadrotor unmanned aerial vehicle (QUAV) with external disturbance, input saturation and input delay. Firstly, the disturbance observer technique is used to address the external disturbance. Subsequently, the auxiliary system method and Padé approximation technique are used to handle the input saturation and input delay problems, respectively. Then, an ADP algorithm based finite-horizon robust optimal trajectory tracking controller is designed to meet some suitable performance requirements in a finite time. Finally, the Lyapunov method is applied for stability analysis of the whole closed-loop system, simulation tests is carried out for the QUAV to verify the reliability of the proposed robust optimal control policy.