This Thesis objective was to apply Model predictive control (MPC) on a quadcopters using linear parameter varying (LPV) techniques. In order to do so the non-linear mathematical model of the quadcopter was put in the Linear Parameter Varying (LPV) form in order to be able to use the most basic Model Predictive Control (MPC) strategy, developed for linear systems. After applying the MPC strategy, the aim was to make the quadcopter track a given trajectory. Different trajectories were tested and validated. Initially, the most important step was to define the coordinate frames that are used to control the quadcopter and to establish the mathematical model of a quadcopter. Once the mathematical model of the quadcopter is developed, the next step was to design the controller. The controller was split into two sub controllers. One controller is responsible for the position variables x, y, z. This position controller controls the position variables by using the state feedback linearization method. Moreover, the attitude controller was used to control the angles using the LPV-MPC control strategy. The proposed strategy turned out to be a success in controlling the quadcopter. All the Quadcopter’s six degrees of freedom are tracked with very small errors. In tracking the x, y, z reference velocity values, one can observe strong overshoot at the beginning of the test period. That can be explained by the fact that the quadcopter starts its journey from quite a long distance away from the trajectory. However, once it reaches the path that it needs to follow, the velocities of the quadcopter stabilize and track the reference values very smoothly. Everything was done keeping in mind that the LPV-MPC controller needs time to push the state angles towards its reference values. Therefore, the attitude controller must work at a higher frequency compared to the position controller