Grid-connected inverters (GCI) are widely used to feed power from renewable energy distributed generators into smarter grids. Repetitive control (RC) enables such inverters to inject high quality fundamental-frequency sinusoidal currents into the grid. However, digital RC which can get approximately zero tracking error of any periodic signal with known integer period in steady-state, cannot exactly track or reject periodic signal of frequency variations. Thus digital RC would lead to a significant power quality degradation of GCIs when grid frequency varies and causes periodic signal with non-integer periods. In this research paper a frequency adaptive repetitive control scheme (FARC) at a predefined sampling rate is proposed to deal with all types of periodic signal of variable frequency. A fractional delay filter which is based on Lagrange interpolation is used to estimate the fractional period terms in RC. This proposed FARC controller offers the fast, during process modification of fractional delay and fast revise of filter parameters, and then provides GCIs with a simple but very accurate real-time frequency adaptive control solution to the injection of high quality sinusoidal current under grid frequency variations. A case study a three-phase GCI is conducted to testify the validity of the proposed strategy.