Research and development in the field of UAVs have witnessed a significant surge lately. This study aims to design a control strategy for tracking the trajectory of unmanned aerial vehicles (UAV) Hexacopter based on sliding mode control theory. First, the non-linear translational and rotational mathematical model of the Hexacopter is initially derived using the Newton-Euler formulation. Subsequently, a nonsingular fast terminal sliding mode controller (NSTSMC) is developed to enable the system to accurately follow the given flight trajectory, while accounting for variations in the three orientation angles. For that, six sliding manifolds are designed to have a fast dynamic response, and their stability analysis is verified using the Lyapunov direct method. To enhance the robustness of the flight controller and the control quality, external disturbances are taken into account in the modeling and control development, and chattering reduction is also taken into account. The proposed control's validity and performance are evaluated in MATLAB/Simulink compared to the classical PID controller. The comparative simulation results indicated that the aircraft under the NSTSMC could effectively flow along the predetermined trajectory, and counteract disturbances that had a negligible impact on the path without requiring undue exertion.