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In this paper, a new observer, named as the higher-order observer, is proposed for simultaneously estimating the system state and disturbance. When the usual assumptions on the disturbance are satisfied, the magnitudes of the state and disturbance estimate errors of the system are proved to be on the order of <inline-formula> <tex-math notation="LaTeX">$O(T^{3})$ </tex-math></inline-formula>, which is much less than <inline-formula> <tex-math notation="LaTeX">$O(T^{2})$ </tex-math></inline-formula> produced by the proportional-integral-observer (PIO). The simulation results also show the effectiveness and superiority of the proposed method.