In this paper, the method of non-singular backstepping terminal sliding mode (NSBSM) is used to control the motion of an unmanned aerial vehicle (quadrotor). In the first step, the dynamic equations of quadrotor will be derived by considering all of the effective parameters. The purpose of controller is to achieve proper tracking for desirable positions (x, y, z), yaw angle (Y), and sustainability of the roll and pitch angles notwithstanding of external disturbances. In practical, due to the need for complete information about system states, the usage of controlling methods may be limited. Noise is an indispensable part even all the states of system be available. It should be noticed that usage of a large number of sensors in order to measure states, cause the whole system to be complex and expensive in practical. For this purpose, the Extended Kalman Filter (EKF) has been used as an observer. The EKF in the control structure is used as observer states of the system and noise reduction in these modes. Therefore, simultaneous use of the controller-observer is suggested for controlling and estimating quadrotor states. The design method is based on the stability of Lyapunov and also the simulation results show the good performance and robustness of the observer-controller.