This paper presents design and implementation of Model Based Predictive Controller (MPC) for a novel Bi-Rotor Moving Mass Controlled (MMC) Unmanned Aerial Vehicle (UAV). Due to the strict constrained control inputs in this type of UAV, it is necessary to take into account the constrained controller design and un-constrained control methods are not applicable. MPC controller which is designed based on the linear model by considering control constraints, is implemented on the nonlinear model of the UAV’s planar motion and compared with LQR controller, the simulation results show significant performance of this controller in control of the UAV while respecting control constraints.