Increasing demands for autopilot systems in order to help pilots in every kind of maneuver and avionics caused great researches and investments in this area. One of the most important fields in design and fabrication of the autopilots is control system design. Since these systems are simulators of an experienced pilot commands, we have to find a way in order to omit pilot wrong decisions in any kind of missions. This is a tracking problem with zero steady state errors. In this article design of an airplane autopilot for roll motion using LQR is proposed which use Luenberger observer for flexible model of the system in order to being kept away from instability. This observer had omitted flexible model effects and improved performance of the system, quality of the responses and made robust system against disturbances. The results show pleasant match with desired inputs.