In micro-grid, the quality problems of grid voltage, i.e. unbalance, harmonic pollution and frequency fluctuation, may occur at the same time. In order to maintain synchronization of grid-connected inverter at this particular circumstance, an improved dual second-order generalized integrator (DSOGI) PLL is proposed. The harmonic components of phase and frequency are eliminated by adding closed-loop feedback control of angular frequency. Meanwhile, the precise angular frequency reference is accomplished by means of zero cross detection circuit and relevant soft arithmetic. Moreover, the proposed PLL maintains steady-state precision and dynamic performance in unbalanced, polluted, and frequency fluctuation circumstances at the same time. Simulation results in MATLAB confirm the effectiveness of the proposed method.