The nonlinear disturbance observer (NDO) proposed by W. H. Chen et al. needs an assumption that the disturbance varies slowly relative to the observer dynamics (i.e. (d) over dot(t) approximate to 0), so as to ensure the convergence of the disturbance observer. When (d) over dot(t) not equal 0, however, there is no guarantee of the convergence in theory. To solve the problem, this paper presents a new NDO, namely high-order nonlinear disturbance observer (HONDO), for a nonlinear system with an unknown fast time-varying disturbance (i.e. (d) over dot(t) not equal 0). The HONDO not only inherits all the advantages of the usual NDO, but also guarantees the convergence of the estimated error for a nonlinear system with a fast time-varying disturbance. Therefore, the HONDO proposed in this paper broadens the application scope of the conventional NDOs, thus is a supplement to the theory of NDO. The numerical simulation for the cruise control of an air-breathing hypersonic vehicle further verifies the effectiveness of the HONDO-based control.