This paper addresses the robust attitude control problem for quadrotors subject to model mismatch and disturbances.A dynamic inversion based attitude control scheme is proposed,which consists of an outer loop attitude controller and an inner loop angular acceleration con-troller.The attitude controller is designed based on the Nonlinear Dynamic Inversion (NDI) to pre-cisely linearize the nonlinear dynamics between the angular acceleration and the attitude.An onboard actuator model-based Incremental Nonlinear Dynamic Inversion (INDI) controller is designed in the angular acceleration control loop to improve the robustness against the model mis-match and disturbances.Meanwhile,the onboard actuator model with a modified structure elimi-nates the oscillation phenomenon when the sampling rate of the controller is higher than that of the actuator.Numerical simulations and flight tests demonstrate the effectiveness and robustness of the proposed controller in comparison with the PID controller.