The unmanned aerial vehicle (UAV) flight control system is a typical strongly coupled, underactuated, and nonlinear time-varying system with time-varying parameters. Traditional model predictive control (MPC) has poor applicability in time-varying, underactuated, and state coupled nonlinear systems. To address the issue of poor timeliness in solving UAV flight problems using MPC. This article proposes MPC based on feedback linearization. Firstly, using feedback linearization to transform the UAV dynamics model into a linear time invariant system (LTI). Then, UAV flight controller was designed using MPC. Conduct simulation experiments and result analysis on the flight control of UAV. Compare the simulation results of approximate linearization to verify the control performance of the designed control system.