Trajectory tracking using linear model predictive control (LMPC) ensures optimal tracking of the system trajectory subject to constraints imposed by system dynamics and actuator limitations. Even though the method is attractive for most applications, solving an optimization problem tends to be a computationally intensive task. In order to alleviate the computational cost associated with LMPC, a flatness based model predictive control (FMPC) algorithm is proposed and simulated for a 6DoF UAV. The reduction in the dimension of the optimization problem due to flatness leads to a significant increase in computational efficiency. In order to show the computational advantages of the FMPC algorithm, it is compared with a standard LMPC algorithm.