To track the reference attitude angles and angular accelerations in the presence of strong uncertainties and disturbances, a new robust generalized predictive control (GPC) law is presented for a near-space hypersonic vehicle (NHV). The control law consists of the optimal GPC law and radius basis function disturbance observer (RBFDO). The output prediction defined on finite horizon is carried out via Taylor series expansion. The unmodeled dynamics and unknown disturbances in flight are estimated by the RBFDO, and the stability analysis of the close-loop system is provided also. The robust GPC law of the NHV proves to be able to attain the optimal index in mathematics. The simulation results show satisfactory performance of the presented controller for entry attitude tracking control, and the robustness to parameters variations and the disturbance rejection are successfully accomplished.