This thesis describes the simulation of the longitudinal motion control by using a proportional-integral-derivative (PID) controller, linear quadratic regulator (LQR) controller and proportional LQR (P-LQR) controller. The non-linear model of the motion is linearized and is implemented in the controllers to elucidate the longitudinal motion at various flight profile, speed and altitude. The control performance of an aircraft is at best condition when the aircraft reaches the desired response instantaneously and precisely. However, the performance of currently available controllers is not ideal and a 10% improvement in controller performance can lead to a significant effect. Hence, P-LQR controller is developed. Three steady state level flights of Boeing 747-100 are investigated in this study. The proposed controller improves the response time of the control system significantly compared with other existing controllers. A simulation is done by using MATLAB to visualize the performance difference of the controllers.