Abstract: This paper mainly focused on transient stability issues of the weak grid connected voltage source converter (WG-VSC) system under phase-locked loop synchronization. Firstly, the linear matrix inequality optimization method was applied to construct the largest estimated domain of attraction (LEDA) of the WG-VSC system. Compared with the LEDA constructed by the energy function method based on the LaSalle invariant principle and the LEDA constructed by the sum-of-square programming method, the proposed method was less conservative in characterizing LEDA. Then, for ensuring the transient stability during the fault ride-through process, the concept of the feasible region of current settings of the WG-VSC system under symmetrical grid faults was proposed. Furthermore, based on the LEDA characterized by the proposed linear matrix inequality optimization method, the solution algorithm of this feasible region was derived. The influence of typical parameters on this feasible region was analyzed. It should be noted that this feasible region can provide practical guidance for the current settings under faults. Finally, a detailed switching model of WG-VSC system based on PSCAD/EMTDC was built. Detailed simulation results have verified the LEDA constructed and the feasible region of current settings.