A robust model predictive control algorithm which costs little online computation for the fixed-wing unmanned aircraft during its perching maneuver process is investigated based on the UAV’s longitudinal motion. First, the nonlinear dynamic system is linearized along the reference trajectory in order to establish the piecewise linear system. Second, considering the external wind disturbance, a tensor product model is further constructed. Then, using the concept of asymptotically stable elliptical invariant set, the method of “offline design, online synthesis” is adopted to design the tracking trajectory control law with less online calculation. The stability of the system is analyzed by combining the robust predictive control and the global stability analysis method of the switching system. Finally, the maneuvering process of fixed-wing UAV under external wind disturbance is simulated. The simulation results show that the designed tracking controller costs less on-line calculation and provides good control effect.