The continuous growth of air transportation demand and the tightness of airspace resources in the terminal area of a hub are becoming more and more prominent. A dynamic programming approach to limit optimization （DPALO） is proposed to solve the arrived landing problem （ALP）. First， a discrete mathematical model of flight landing scheduling with time window constraints is established， and a recursive formula for solving ALP with a fixed order is derived. The flight time window is optimized by combining the ALP problem characteristics with the constraints， and it is proved that the proposed method does not affect the solution of the optimal value of the model. Second， elite genetic algorithms， particle swarm algorithms， the linear loop swapping and the linear loop interpolation are applied to adjust the flight sequences and then to finding an optimal solution. Finally， validation is performed on the OR-Library dataset. The experimental results show that using the elite genetic algorithms to adjust the flight landing sequence， DPALO outperforms the best known values （BKV）， the bionic algorithm （BA） and the displacement decision algorithm （DDA） and obtains similar results to those of the cellular automata optimization approach （CAO）， the tight subsequence algorithm （CSA）， and the rolling horizon framework of hybrid particle swarm optimization local search algorithm （RH-HPSO-LS）. The time efficiency of DPALO achieves milliseconds in time on the small sample dataset， and it is improved by 76.88%， 89.11%， and 78.28% on the large sample dataset in comparison to CSA， CAO， and RH-HPSO-LS， respectively.