Abstract: A grid-connected converter (GCC) is prone to transient instability under weak grid faults. However, it is very difficult to analyze the transient stability of GCC, due to the characteristics of high-order, nonlinear and strong coupling. Most of the existing works only study the phase-locked loop system and ignore the influence of current control, which cannot fully reflect the transient instability mechanism of GCC in weak grid. To cope with the issue, this paper studies the transient stability of GCC under weak grid faults, while considering the control dynamics of PLL and current loop. Firstly, the singular perturbation model of GCC is established, and then the original high-order model can be simplified to the low-order fast and slow subsystems. Afterward, the stability of the fast and slow subsystems is analyzed by Lyapunov's first and second methods, respectively. On this basis, the effects of various factors on transient stability are revealed, and some guiding principles for control parameter optimization are given. Finally, the analysis results are validated by experiments.