[Objective] With the continuous increase in the penetration of renewable energy generation, the grid-forming (GFM) converter, owing to their capability to actively support voltage and frequency, are regarded as a key technology for enabling the reliable integration and stable operation of power systems with high shares of renewable energy. However, due to the limited overcurrent withstand capability of power semiconductor devices, when voltage sags or other faults occur in the power grid, the GFM converter prone to large power angle deviations, loss of synchronization, and transient overcurrent, thereby posing significant challenges to stable operation. [Methods] Aiming at the above problems, based on the equivalent impedance model of the GFM converter and combined with the vector diagrams of system voltage and output current before and after the fault, this paper systematically analyzed the generation mechanism of overcurrent during the fault process and the influence of voltage amplitude and power angle variations on the fault current amplitude. On the basis of the above analysis, a comprehensive control strategy that took into account both transient synchronization stability and fault overcurrent suppression was proposed. The proposed strategy adaptively reduced the active power reference value to enhance the power angle stability of the system. Meanwhile, to achieve overcurrent mitigation throughout the entire fault process, the strategy implemented fault current magnitude constraints along with a combined control approach. This approach synergized internal voltage reference regulation for steady state fault current management and virtual impedance for surge current suppression. [Results] Finally, the rationality and effectiveness of the proposed strategy were verified through comparative tests on an experimental platform. The experimental results indicated that, compared with conventional methods, the proposed strategy had significant advantages in enhancing the transient performance of the grid-forming converter. It was able to maintain the power angle stability of the system under various grid fault conditions, effectively suppress the fault current, and ensure that both the surge current and the steady-state fault overcurrent magnitude were below the preset thresholds. [Conclusion] The comprehensive fault ride-through strategy for the GFM converters considering current constraints proposed in this paper takes into account both power angle stability and overcurrent suppression, and can significantly improve the operational reliability of grid-forming converters under complex grid fault conditions.