Autonomous underwater vehicles are submarines which are extensively employed for underwater exploration and scientific missions. These vehicles are highly nonlinear, their parameters are uncertain and they are accompanied with unmeasurable disturbances. These characteristics made the trajectory tracking control of autonomous underwater vehicles to be a challenging task. Among various nonlinear controllers, sliding mode control has been extensively investigated for the trajectory tracking control of autonomous underwater vehicles and it provided good control performance. However this controller has chattering effect and its convergence is asymptotic. The chattering problem was relieved by using a smooth switching function or higher order sliding modes, and finite time convergence was obtained by introducing adaptive nonsingular terminal sliding mode control. But this terminal sliding mode control exhibits lower convergence speed than the conventional one when the states are far from the origin. This can be resolved by using adaptive fast nonsingular terminal sliding mode which had global fast convergence in the sliding phase. In this thesis, to obtain fast convergence at sliding phase, an adaptive fast non singular terminal sliding mode control is proposed for trajectory tracking of autonomous underwater vehicles. The kinematics and dynamics equations for autonomous underwater vehicles were first developed. Then by taking the error dynamics, the control law is proposed. In addition, stability of the proposed controller is proved via Lyapunov stability. When the system modeling and controller design procedure is finished, MATLAB was used to verify the performance of the proposed controller. Simulation results revealed the superior performance of the proposed controller. When exponential reference trajectory is taken, the reaching time was 15 sec and 9 sec for the proportional integral sliding mode control and proposed controller respectively. Where as for circular reference trajectory, the reaching time was 16.75 sec and 10.8 sec for the proportional integral sliding mode control and proposed controller respectively.