In this paper, a backstepping controller is presented for quadrotor system to follow a predefined trajectory without the knowledge of dynamic parameters in the control algorithms. By dividing the quadrotor systems into several subsystems, the idea of nominal control input is presented to modify the quadrotor input force and torque. Subsequently, the backstepping control technique is developed for the nominal controls with the adaptive laws to estimate unknown dynamic parameters. Both the mass and moment of inertia are coped with by using adaptive laws. Stability and tracking performance of the proposed closed-loop system are proved by using Lyapunov theorem that the tracking errors converge to the origin asymptotically. Numerical examples are presented to show the quadrotor system tracking a desired trajectory efficiently.