This paper establishes a small-signal impedance model of the doubly fed induction generator (DFIG) system under weak grid faults taking the dynamic of controller and impedance controller into account. Based on the impedance model, the instability mechanism of the DFIG system during LVRT is analyzed using the generalized Nyquist criterion (GNC). The analysis result shows that the small-signal instability of the DFIG system is due to the DFIG-based wind turbines (WTs) in account of the control showing the negative damping characteristics during grid fault. The small-signal stability of the DFIG system can be improved by changing the bandwidth of the phase-locked loop (PLL). The simulation results verify the correctness of the analysis.