A scheme of robust fault reconstruction via the sliding mode observer(SMO) is proposed, which is used for a class of uncertain nonlinear Lipschitz system with the simultaneous actuator and sensor faults. Firstly, an orthorhombic matrix and a filter are introduced, and the augmented system is constructed, then the gain matrix of the robust SMO is calculated by the multi objective convex optimization under linear matrix inequalities. Meanwhile, an adaptive law is added in the sliding mode gain, to make the state estimated error asymptotic stable, and the sliding mode movement reaches the sliding mode surfaces in the limital time. The reconstructed algorithm is given, which includes both actuator and sensor faults. Finally, an example is presented to illustrate the effectiveness of the proposed approach.