Grid-forming inverters(GFIs), which can mimic the behaviors of conventional synchronous generators to provide the frequency and voltage support for the electricity grids, face the challenge of overcurrent during grid faults due to the voltage-source output characteristics. The power semiconductors of inverters are incapable to withstand fault current and easily destroyed. To tackle the overcurrent dilemma encountered by GFIs during voltage drops, this paper proposes an adaptive virtual impedance-based fault current limiting strategy. This adaptive strategy can adjust dynamically the virtual impedance value in real-time based on the magnitude of fault currents, and thereby suppress fault currents effectively. To analyze the impacts of the adaptive impedance on the stability of GFIs, an impedance model composed of the adaptive impedance, grid and voltage control loops, is established in the dq reference frame. The influence of the adaptive virtual impedance control parameters on the stability of the grid-forming inverter system is evaluated through the generalized Nyquist criterion. The efficacy of the proposed adaptive virtual impedance strategy in fault current limitation and the accuracy of the stability analysis are validated through the comprehensive simulation results carried out in Matlab/Simulink and OPAL-RT semi-physical platform.