Modern grid codes require wind turbines (WTs), e. g., type-4 WTs, to have low voltage ride-through (LVRT) capability, and recently, great attention has been attracted on the stability issues of WTs during the period of the LVRT. In this paper, we investigate the influences of the LVRT control on the stability of type-4 WTs under severe voltage sags in very weak grids. First, by proposing a novel quasi-staticmodelingmethod, we explore the existence of the WT's equilibrium during the LVRT. It is shown that theWT can lose the equilibrium under certain circumstances, leading to instability of the wholeWT system. Furthermore, we use the small-signal analysis to illustrate that even there exists an equilibrium, theWT can become linearly unstable due to the dynamics of the current references generated by the LVRT control. We propose an enhanced LVRT control strategy to deal with these instability problems. Simulations verify our analysis and effectiveness of the proposed control strategy.