Convergence rate is a key performance index for flight vehicles, and accelerating it remains a critical open issue. In this paper, a fast robust integrated guidance and control scheme for flight vehicles based on convergence rate estimation mechanism is proposed, which improves the control performance and interception accuracy of flight vehicles. In the fast robust control scheme, a convergence rate indicator for integrated guidance and control systems is developed to measure the impact on convergence rate imposed by model nonlinearities and couplings within flight vehicles. Based on the indicator, the influences on convergence rate are transformed and injected into controllers to accelerate the convergence of flight vehicles. The unmatched lumped uncertainties in flight vehicle dynamics are addressed by a backstepping control method and finite-time convergence disturbance observers, which improves the robustness of the vehicle’s control system. Furthermore, the stability analysis of the closed-loop system is performed via the Lyapunov stability theorem. Extensive numerical simulations are conducted to verify the effectiveness and interception performance of the proposed method, and the comparison results confirm that it outperforms three other recently developed robust control methods.