The LCL grid-connected inverter makes extensive use of capacitive current feedback active damping because of its good resonance peak suppression performance. However, the existence of control delay under digital control weakens the effect, resulting in possible instability of the system. To enhance the robustness of capacitive current feedback control, a delay compensation strategy for an LCL grid-connected inverter is proposed in this paper. The strategy uses the improved Newton interpolation to predict the actual control signal, which is equivalent to providing the leading phase for the forward channel of grid connected current loop. In such way, it can maintain the effectiveness of inverter active damping and strengthen the stability of the system. Furthermore, compared with the traditional Newton interpolation delay compensation, the proposed strategy integrates the computation delay and pulse width modulation delay, thus expanding the control delay compensation range. The under compensation problem caused by limited compensation ability can be avoided. Finally, simulations and experiments confirm the effectiveness of this proposed control strategy.