In the distributed grid, it is important to synchronize the grid-connected inverters with the grid. The second-order generalized integrator-based phase-locked loop (SOGI-PLL) is a single-phase PLL with relatively outstanding overall performance. However, its performance is not satisfactory under the condition of large bandwidth and weak grid due to the nonlinearity of coordinate transformation and the coupling caused by frequency feedback path. Therefore, this paper proposes an efficient frequency detection method based on three consecutive sample (3CS) to improve the performance of traditional SOGI-PLL, and adds a low-pass filter in the frequency detection branch to improve the frequency detection accuracy. Then, using the harmonic linearization modeling method, the model of the proposed scheme in the frequency domain is established. Finally, better behavior and stability of the proposed improved strategy is verified theoretically and experimentally, and compared with the traditional SOGI-PLL. Besides, experimental results show that the proposed strategy not only greatly expands the bandwidth of PLL and improves the dynamic performance, but also greatly improves the robustness of the inverter under large grid impedance.