Nowadays, small structured unmanned aerial vehicles (UAVs) with four-rotor (Quadrotor) appear in every part of human life works. As the usage areas of the air vehicles become widespread, the development of controller structures which allows the quadrotor to track a specified trajectory precisely is a new research area of interest for researchers. In this work, the nonlinear mathematical model of a four-rotor UAV is obtained by using Newton-Euler method. In the trajectory tracking system of this quadrotor, a new controller structure which is called Robust Adaptive Backstepping Global Fast Dynamic Terminal Sliding Mode Controller (RABGFDTSMC) is designed. In this controller structure, the control process is divided into two subsystems in order to provide position and attitude control. RABGFDTSMC is applied to the fully actuated and underactuated subsystems individually. Coefficients of the controller is obtained by using pre-defined characteristic equation. Besides, overall system stability is proved with the Lyapunov function. To demonstrate the effectiveness of the proposed controller, simulation experiments are conducted in MATLAB/ Simulink environment. The simulation results of the proposed controller are compared with the global fast dynamic terminal sliding mode controller by means of trajectory tracking performance in steady-state and transient phases. As a result, the proposed controller RABGFDTSMC method proved its robustness according to the smaller steady state error with less oscillations and more precise flight performance in trajectory tracking.