In order to improve the quality of grid-connected current, the full feed forward control of grid voltage is often used to increase the output impedance of inverter. However, due to the influence of digital control delay, not only the harmonic suppression effect is weakened, but also the negative phase shift of the output impedance, which deteriorates the stability of the inverter in the weak network. In this paper, a time-delay compensation and weighted feedforward control strategy is proposed, in which a series of quasi-resonant items are added to the full feed forward circuit, and only the feedforward background harmonics appear at the frequency. By designing the quasi-resonant term, not only the phase delay introduced by the digital control can be compensated, but also the higher output impedance at the background harmonic frequency can be obtained, and the negative phase shift of output impedance can be reduced, and to improve the stability of the inverter in a weak power grid. Finally, a 6kw inverter prototype is built, and the validity and correctness of the proposed control strategy are verified by experiments.