In line-commutated converter-based high-voltage direct current (LCC-HVDC) systems, subsequent commutation failures are prone to occur following AC faults at the receiving end, seriously threatening the secure operation of the systems. To enhance the capability of suppressing subsequent commutation failures, this paper proposes a predictive optimization control method based on the dynamic extinction angle equation. By analyzing the dynamic characteristics of DC current and extinction angle during the recovery phase following the initial commutation failure, a differential dynamic equation for the extinction angle is established. Using phase-plane analysis, the mechanism of subsequent commutation failure is revealed: when the extinction angle decreases to a critical threshold and its rate of change remains negative, commutation failure occurs. To improve the suppression capability, a predictive optimization control method based on the dynamic extinction angle equation is proposed. A real-time prediction criterion is designed to dynamically calculate the extinction angle trend using the effective AC voltage magnitude and its rate of change. Simultaneously, a dynamic compensation control strategy is developed, in which a compensation term is added to the fixed extinction angle control to continuously adjust the reference in real time. Simulation results based on the CIGRE benchmark model demonstrate that the proposed prediction criterion achieves significantly higher accuracy than conventional methods under both three-phase and single-phase grounding faults. Moreover, the proposed optimal control strategy effectively suppresses subsequent commutation failures and significantly enhances the system’s transient stability.