When a doubly-fed induction generator (DFIG) is connected to a weak grid, the coupling between the grid and the DFIG itself will increase, which will cause stability problems. It is difficult to maintain the tracking accuracy and robustness of the phase-locked loop (PLL) in the weak grid, and the risk of instability of the current-controlled DFIG (CC-DFIG) system will increase. In this paper, a new type of voltage-controlled DFIG (VC-DFIG) mode is adopted, which is a grid-forming structure that can independently support the voltage and frequency with a certain adaptability in the weak grid. A small-signal impedance model of the VC-DFIG system is also established. The impedance of DFIG inevitably generates coupling with the grid impedance in the weak grid, especially in parallel compensation grids, and results in resonance. On the basis of the VC-DFIG, impedance stability analysis is performed to study the influences of the control structure and short-circuit ratio. Then, a feedforward damping method is proposed to modify the impedance of the VC-DFIG system at resonance frequencies. The proposed fractional order damping is utilized, which can enhance the robustness and rapidity of resonance suppression under parameter fluctuations. Finally, the experimental results are presented to validate the effectiveness of the proposed control strategy.