A novel scheme for disturbance observer is designed for an extended class of strict-feedback nonlinear systems with possibly unbounded, non-smooth, and state-independent compounded disturbance. To overcome these problems in disturbance observer design, the typical slide mode differentiators are improved by introducing hyperbolic tangent function to make the signals smooth, and then the improved slide mode differentiators are constructively used to estimate the errors of variables in the presence of disturbances. The unbounded, non-smooth or state-independent disturbances are therefore able to be eliminated by using the estimated variable errors. Thus, the bounded or differentiable conditions for disturbance observer design are removed. Furthermore, the convergence of the new disturbance observer is rigorously proved based on Lyapunov stability theorem, and the tracking error can be arbitrarily small. Finally, the simulation results are given to validate the feasibility and superiority of the proposed approach.