For the chattering problem in the fault estimation using the traditional sliding mode observation, the second order sliding mode observation based on the super-twisting algorithm is designed to estimate the fault stably. In order to avoid the cumbersome process of proving the stability of the super-twisting algorithm using the geometric method or the homogeneity, a Lyapunov function is adopted to prove the stability of the super-twisting algorithm. The given fault estimation result can be calculated on-line. Moreover, the result overcomes the drawbacks of introducing the delay or the new parameter caused by the traditional methods. Finally, the proposed method is applied to a certain type of flight control systems, and the results show its effectiveness.