This paper proposes a PLL based on double second-order generalized integral (DSOGI-PLL) of abstracting grid voltage phase quickly and accurately for low accuracy of traditional PLL in the case of the unbalanced grid voltage in grid-connected PV systems. Firstly, the principle of the SOGI, which can effectively extract the grid voltage positive sequence component, to be used as a quadrature signal generator is analyzed. Secondly, to eliminate the influence of DC offset, an improved structure of SOGI is proposed. So a novel PLL applicable to the case of unbalanced grid which can eliminate the influence of DC offset is shown. Finally, the effectiveness of the proposed PLL is varied by simulation and experiment.