Repetitive control (RC) is gradually used in inverters tied with weak grid. To achieve the zero steady-state error tracking of inverter current and compensate the harmonic distortion caused by frequency fluctuation, a frequency adaptive (FA) control scheme for LCL-type inverter connected with weak grid is proposed. This scheme adopts a proportional resonance (PR) controller in parallel with RC (PRRC) to overcome the disadvantages caused by RC inherent one-cycle time delay. A fractional delay (FD) filter based on the Newton structure is proposed to approximate the fraction item of fs/f, where fs and f are sample frequency and grid frequency, respectively. The structure of the proposed FD filter is relatively simple; moreover, coefficients of the filter maintain constant so as not to need online tuning even when grid frequency fluctuates, which decreases the computational burden considerably. The feasibility and effectiveness of the proposed FA control scheme, named as Newton-FAPRRC, are all verified by the simulation and experimental results.