In this paper, a nonlinear robust Fast Terminal Sliding Mode Controller (FTSMC) is designed to control and stabilize a new reconfigurable Unmanned Aerial Vehicle (UAV) in the presence of uncertain and variable parameters. The studied UAV is an over-actuated system due the number of actuator control inputs. It can modify the length and the angles between its four arms in different ways, which result an important variation in its Center of Gravity (CoG), inertia, and control matrix. The proposed FTSMC offers many advantages such as, reaching the desired states in a finite-time unlike the conventional sliding mode, robustness vis-a-vis uncertain and unknown parameters, fast convergence towards the sliding surface, high accuracy and reducing the chattering phenomena. Furthermore, the closed-loop stability of the this UAV is ensured by the Lyapunov theory. The eight actuators used to rotate and extend the UAV arms are controlled by simple Proportional Integral Derivative (PID) controllers. Lastly, the robustness and efficiency of the proposed controller are evaluated through a flight scenario, where the UAV geometric parameters are variable over time.