This paper analyzes the characteristics of the trajectory tracking control problem of the manipulator and establishes a two-degree-of-freedom manipulator dynamic model. In order to solve the problem that generalized predictive control(GPC) algorithm is difficult to apply to nonlinear systems, a feedback linearization-based generalized predictive control(FL-GPC) algorithm framework is designed. The bottom layer of the algorithm is the linear system predictive control and the non-linear term is replaced by the estimated value. The upper level is iteratively revised estimates and the non-linear term is estimated using the iterative calculation method. Finally, the FL-GPC algorithm is used to simulate the static and dynamic trajectory tracking tasks of a two-degree-of-freedom manipulator. Simulation results show that the algorithm can perform effective manipulator trajectory tracking control.