The installed capacity of renewable energy generation has continued to grow rapidly in recent years along with the global energy transition towards a 100% renewable-based power system. At the same time, the grid-connected large-scale renewable energy brings significant challenges to the safe and stable operation of the power system due to the loss of synchronous machines. Therefore, self-synchronous wind turbines have attracted wide attention from both academia and industry. However, the understanding of the physical operation mechanisms of self-synchronous wind turbines is not clear. In particular, the transient characteristics and dynamic processes of wind turbines are fuzzy in the presence of grid disturbances. Furthermore, it is difficult to design an adaptive fault ride-through (FRT) control strategy. Thus, a dual-mode switching FRT control strategy for self-synchronous wind turbines is developed. Two FRT control strategies are used. In one strategy, the amplitude and phase of the internal potential are directly calculated according to the voltage drop when a minor grid fault occurs. The other dual-mode switching control strategy in the presence of a deep grid fault includes three parts: vector control during the grid fault, fault recovery vector control, and self-synchronous control. The proposed control strategy can significantly mitigate transient overvoltage, overcurrent, and multifrequency oscillation, thereby resulting in enhanced transient stability. Finally, simulation results are provided to validate the proposed control strategy.