Trajectory optimization is a key element of efficient flight analysis and synthesis. This paper studies dynamic programming (DP) application to airliners' flight trajectory optimization. A four dimensional trajectory optimization tool is developed for airliners' flight. An acceleration technique called moving search space dynamic programming is included to relax the computational time problem in DP. Application examples are discussed to demonstrate versatility and flexibility of the DP trajectory optimization. Two basic problems of conflict free trajectory optimization, the fuel minimum flight with a constraint of arrival time and the optimal trajectory with an inequality constraint of safe separation with other aircraft, are studied to evaluate impacts of the equality and inequality constraints on the performance. Next, the tool is applied to actual flight data which are reconstructed from GPS logger data measured in a cabin of an airborne aircraft. Fuel consumption and flight time of actual airliner flights are compared with those of the optimal trajectories. The optimal trajectory provides potential benefit possibly gained by improving the present flight operation and air traffic control.