The inverter-side current as a feedback parameter is a commonly used type of inverter which uses indirect current control, it has better stability than direct current control. However, in practical applications, the inverter usually works in the weak grid condition, the stability of grid-connected inverter will be greatly reduced. Taking the three-phase LCL inverter-side current feedback grid-connected inverter as an example, this paper analyzes the mechanism of the system stability degradation by using the frequency domain analysis method, and proposes to install a Second-Order Generalized Integrator (SOGI) in the grid voltage feedforward path. This strategy can attenuate the additional positive feedback associated with the impedance, which is introduced by the grid voltage proportional feedback, thereby improving system stability under weak grid. Finally, through the grid-connected inverter model and experiments, the effectiveness of the proposed control strategy is verified. This work is supported by National Natural Science Foundation of China (No. U1804143 and No. 61703144), Key Science and Technology Project of Universities and Colleges of Henan Education Department (No. 17A470010), and Fund of Henan Mine Electrical and Electronic Device and Control Innovation Scientific and Technological Team (No. CXTD2017085).