Grid-forming inverters may suffer instability issues while operating in stiff grid conditions, leading to sub-synchronous oscillation in the system. To investigate the root cause of instability behavior, this paper establishes a simplified small-signal model in the dq frame to capture the dynamics of the inverter in the sub-synchronous frequency range. The dominant factors inducing sub-synchronous oscillations are analyzed. It is found that the phase margin of the loop vq–θ decreases and even becomes insufficient with the increase of grid strength, resulting in sub-synchronous oscillation. To address this issue, a phase compensation strategy is proposed to ensure the system stability. Finally, the accuracy of the analyses and the effectiveness of the proposed phase compensation strategy are validated through simulations.