Aiming at studying the system stability of the grid-connected inverter under unbalanced grid, this paper establishes the small-signal model of dual second order generalized integrator phase locked loop(DSOGI-PLL), and derives the sequence impedance model of the grid-connected inverter with DSOGI-PLL. Then, the system stability under unbalanced grid is analyzed by using the generalized Nyquist criterion. It is found that the use of DSOGI-PLL can significantly improve the system stability under unbalanced grid, due to the lower bandwidth of DSOGI-PLL. Finally, the corresponding simulation and experimental verifications are carried out, and the results prove correctness of the theoretical analysis in this paper.