The high bandwidth of a phase-locked loop (PLL) can deteriorate the small-signal stability of a voltage-sourced converter (VSC) under a weak grid condition. This instability can occur for a VSC operating as both a rectifier and an inverter, but the root causes can differ for the two. This study, through modal analysis, demonstrates that different approaches are required depending on the power flow direction to resolve the instability. Subsequently, an analysis of the rectifier dynamics is set as the primary target, and the instability characteristic is investigated via a new approach that utilizes the open-loop transfer function of the power control loop. Consequently, it is discovered that the high-bandwidth PLL reduces the reactive power compensation for the AC system and results in a severe voltage drop. A novel parallel voltage filter technique is proposed to overcome this instability. The performance of the proposed method is verified in the frequency- and time-domain analyses. The results indicate that the proposed method effectively improves stability without major modifications to the control system.