Power electronic devices are critical components for interfacing renewable energy sources (RES) to the utility grids. The safe and proper operation of the grid-connected inverter (GCI) becomes a substantial challenging under grid fault conditions. For this purpose, this paper presents a sequence based control strategy to enhance the dynamic behavior of the GCI under unbalanced grid voltages. The main contribution to existing methods, dual adaptive filter based sequence extraction method is proposed to fast separate positive and negative sequence of unbalanced three phase signals. The proposed sequence extractor reduces settling time significantly, which is less than one cycle time delay. This novelty of the improved sequence extractor is also compared to another extractor based on fast Fourier transform (FFT). A set of simulation results has been presented to verify the effectiveness of the proposed sequence based control strategy.