On the basis of nonlinear dynamic inversion theory, a novel scheme combining sliding-mode control and backstepping is proposed for missile attitude control. In order to handle matched and unmatched uncertainties caused by unmodeled dynamics and variations of aerodynamic coefficients, a linear extended state observer (LESO) is introduced to estimate the uncertainties and the evaluated errors are compensated at each step of the backstepping design procedure. The stability of the closed-loop system is demonstrated based on Lyapunov theory. Simulation results show that the proposed scheme can guarantee the excellent tracking performance and the strong robustness against aerodynamic derivative variations.