In this paper, a novel Model Reference Adaptive Control (MRAC)-based hybrid control algorithm is presented for the trajectory tracking of a tri-rotor Unmanned Aerial Vehicle (UAV). The mathematical model of the tri-rotor is based on the Newton-Euler formula, whereas the MRAC-based hybrid controller consists of Fuzzy Proportional Integral Derivative (F-PID) and Fuzzy Proportional Derivative (F-PD) controllers. MRAC is used as the main controller for the dynamics, while the parameters of the adaptive controller are fine-tuned by the F-PD controller for the altitude control subsystem and the F-PID controller for the attitude control subsystem of the UAV. The stability of the system is ensured and proven by Lyapunov stability analysis. The proposed control algorithm is tested and verified using computer simulations for the trajectory tracking of the desired path as an input. The effectiveness of our proposed algorithm is compared with F-PID and the Fuzzy Logic Controller (FLC). Our proposed controller exhibits much less steady state error, quick error convergence in the presence of disturbance or noise, and model uncertainties.