Anti-disturbance control problem is studied for a class of nonlinear strict-feedback systems with disturbances. The system disturbances satisfy mismatched condition and represent a class of disturbances with partially-known information. By designing a nonlinear disturbance observer, the nonlinear disturbance observer plus back-stepping(NDOPBS) control strategy is proposed to compensate the disturbances. It is proved that all the signals in the closed-loop system are semi-global uniformly ultimate bounded(SGUUB). Finally, the numerical simulation result demonstrates the correctness and effectiveness of the proposed approach by the comparison with existing methods.