Passivity-based control (PBC) exhibits robustness against parameters shift, providing a substantial level of stability. However, for the LCL-filtered grid-connected inverter (GCI), the conventional PBC (called C-PBC) controller has a narrow control bandwidth due to the control time delay, resulting in poor dynamic performance, especially in the weak grid state. This paper proposes a new PBC (called P-PBC) method to increase the closed-loop bandwidth of the system by setting an appropriate feedback proportional coefficient between the grid-side current and the inverter-side current. By extending the closed-loop bandwidth of the system, the proposed P-PBC method offers improved dynamic performance, particularly in challenging grid conditions. In addition, a state observer is also employed to reduce sensors, which saves costs and enhances the system's reliability. A 110 V/50 Hz/3 kW/3-phase experimental setup has been developed using the dSPACE DS1202 platform to validate the effectiveness of the proposed control method.