The fourth-order generalised integrator is very suitable for single-phase phase-locked loop because it can provide orthogonal signal conveniently and block harmonic voltages effectively. In the conventional fourth-order generalised integrator based phase-locked loop, the resonance frequency of fourth-order generalised integrator needs to be adjusted according to the grid frequency. To improve the phase-locked loop performance, a non-adaptive fourth-order generalised integrator is suggested for single-phase system, and this paper presents a correction method. According to the estimated grid frequency, the amplitude imbalance and phase error caused by non-adaptive fourth-order generalised integrator can be calculated, and two adaptive units are added to deal with the problems. Moreover, the small-signal model of the proposed phase-locked loop is carried out, and the control parameters are tuned. Compared to conventional fourth-order generalised integrator based phase-locked loop, the proposed phase-locked loop shows a better performance, which is verified through simulation and experimental results.