Dynamic inversion (DI) is a control synthesis technique that steers the system states to track the desired trajectory by cancelling the original dynamics. However, it is impossible to achieve perfect cancellation of the original dynamics in real applications, robustness problem must be considered in designing DI controller. In this paper, robust dynamic inversion (RDI) control strategy based on sliding mode control (SMC) is proposed. Different from the previous works of achieving robustness in DI controller, the proposed RDI controller is designed inherently robust. Moreover, robust observer strategy based on the RDI controller is also proposed in this paper. Numerical simulations with application to the AV-8A Harrier aircraft demonstrate the effectiveness of the proposed method.