Division-summation (D-Sigma) digital control has been successfully applied to the single-phase bidirectional inverter with an LC filter, which can coverwide inductance variation and achieve precise inverter current tracking. However, high frequency ripple current injection to the grid cannot be avoided, and an LCL filter is therefore required. Since there typically exist grid voltage harmonics, the injected grid current will contain harmonic components due to the effect of the LCL-filter capacitor. This paper presents an extended application of the D-Sigma digital control associated with a filter-capacitor-current compensation to reduce the injected grid-current harmonics. The control laws of the inverter with the D-Sigma digital control and compensation approach are derived in detail, and the reduction of grid-current harmonics is analyzed. With the proposed approaches, the phase margin between the output impedance of the inverter and grid impedance can be higher than 80 degrees from low to high frequencies, and the inverter can achieve high harmonic voltage rejection ratio up to 39th harmonic, which is relatively suitable for weak grid connection. Experimental results measured from a 5-kW single-phase bidirectional inverter have verified the feasible application of the D-Sigma digital control and proposed compensation.