Quadcopter unmanned aerial vehicle is a multivariable, coupled, unstable, and underactuated system with inherent nonlinearity. It is gaining popularity in various applications and has been the subject of numerous research studies. However, modelling and controlling a quadcopter to follow a trajectory is a challenging issue for which there is no unique solution. This study proposes an optimal hybrid quadcopter control with MPC-based backstepping control for following a reference trajectory. The outer-loop controller (backstepping controller) regulates the quadcopter’s position, whereas the inner-loop controller (Model Predictive Control) regulates its attitude. The translational and rotational dynamics of the quadcopter are analyzed utilizing the Newton-Euler method. After that, the backstepping controller (BC) is created, which is a recurrent control method according to Lyapunov’s theory that utilizes a genetic algorithm (GA) to choose the controller parameters automatically. In order to apply a linear control technique in the presence of nonlinearities in the quadcopter dynamics, Linear Parameter Varying (LPV) Model Predictive Control (MPC) structure is developed. Simulation validated the dynamic performance of the proposed optimal hybrid MPC-based backstepping controller of the quadcopter in following a given reference trajectory. The simulations demonstrate the fact that using a command control input in trajectory tracking, the proposed control algorithm offers suitable tracking over the assigned position references with maximum appropriate tracking errors of 0.1 m for the �� and �� positions and 0.15 m for the �� position.