The LCL-type grid-connected inverter with inverter-side feedback is widely used in practical applications. However, the system stability can be affected by the digital control delay which changes the system phase-frequency characteristics. Therefore, this paper proposes a phase lead compensation based on an adaptive notch filter (ANF). Firstly, the phase lag caused by the control delay is compensated by the phase lead of the notch filter, which avoids the system phase crossing -180° at the resonance frequency; thus, the system stability and its robustness to weak grids are improved. Secondly, the system resonance frequency is estimated by the ANF algorithm, and the notch frequency is dynamically adjusted according to the estimated value; hence, the stability range of the resonance frequency is extended, which enhances the adaptability of the system to LCL parameters variations. Finally, the proposed method is verified by experiments, and the results show that the grid-connected inverter based on the ANF scheme has good stability. Moreover, compared with the traditional notch scheme, the proposed scheme has better robustness to the grid impedance and the LCL parameters variations; thus, it is more conducive to the control of LCL-type grid-connected inverters in weak grids.