Under the weak grid condition, there exists grid frequency shift, which degrades the control performance of a quasi-PR controller with constant parameters. Therefore, it is important to track the grid frequency and enhance the anti-interference capability of frequency locked loop (FLL). Under this background, an adaptive quasi-PR controller strategy based on linear Kalman filter (LKF) is proposed in this paper. First, aimed at the poor anti-interference capability of the traditional FLL, an FLL based on LKF (LKF-FLL) is designed to improve the anti-interference capability of FLL. Then, LKF-FLL is used to track grid frequency, and the resonant frequency of the quasi-PR controller is adjusted in real time to realize adaptive tracking of grid frequency according to the time-varying grid frequency, thus ensuring the control performance of the quasi-PR controller and improving the power quality of grid-connected current. Finally, through simulations and the development of an experimental prototype, the feasibility and superiority of the proposed LKF-FLL strategy was verified.