This paper presents the modelling of a four rotor vertical take-off and landing unmanned air vehicle known as the quadrotor aircraft, Vertical take off and landing, high maneuverability capabilities and indoor/outdoor navigation features make them popular. Besides that, by developing technology, especially in sensor devices, it is easy to obtain one of those vehicles. In this study, firstly, a nonlinear quadrotor model is obtained. Secondly, a linear model is transformed from this nonlinear model. Here, two controllers, Linear Quadratic Tracking (LQT) and (Linear Quadratic Regulator) LQR with integral action, are designed to stabilize the quadrotor system. Motor throttle commands and motor speeds are simulated. Simulation results are presented to demonstrate the performance of the proposed control strategy.