Voltage-source converter (VSC) is crucial in renewable power generation. However, grid seriously affects the stability of VSC. The synchronization stability has attained lots of attention in recent years. Researches on synchronization stability mostly focus on small-signal stability. However, small-signal stability analysis loses its effectiveness for the system with large disturbance, such as grid fault, abrupt weather change, etc. This paper aims to establish the Takagi-Sugeno (T-S) fuzzy model to analyze the large-signal stability of VSC synchronization control by Lyapunov function. The boundary state space and the corresponding membership function are obtained by controlling the original nonlinear model in the sector interval. The influence of system parameters on synchronization stability is analyzed based on Lyapunov function and the domain of attraction (DOA). Finally, the correctness of the model and the stability analysis is verified by MATLAB simulations.