This paper proposes a frequency-locked loop (FLL) scheme for a single-phase grid-connected converter. A second-order generalized integrator (SOGI) based on fuzzy logic (FL) is applied to this converter to achieve precise phase angle detection. The use of this method enables the compensation of the nonlinear characteristic of the frequency error, which is defined in the SOGI scheme as the variation of the central frequency through the self-tuning gain. With the proposed scheme, the performance of the SOGI-FLL is further improved at the grid disturbances, which results in the stable operation of the grid converter under grid voltage sags or frequency variation. The PSIM simulation and experimental results are shown to verify the effectiveness of the proposed method.