Abstract: The filter-cascaded-type frequency-locked loop can reject the influence of the non-fundamental frequency component in the grid voltage on the frequency estimation, so it is suitable for scenarios with severe DC offset and complex harmonics, however, it is difficult to achieve fine dynamic and steady-state performance at the same time. For this reason, the two typical filter-cascaded-types of the frequency-locked loops are analyzed and compared, which are the cascaded second-order generalized integrator frequency-locked loop (CSOGI-FLL) and the fourth-order generalized integrator frequency-locked loop (FOGI-FLL). Based on the derivation of their transfer function and the establishment of their linear model, their control parameters are tuned in the oscillation index method, which proves that the parameter design of FOGI-FLL is more flexible than that of CSOGI-FLL. The rules of the bandwidth and the crossover frequency influencing on the dynamic and filtering performance of FOGI-FLL are analyzed. Base on the analysis, a method for adjusting adaptively the crossover frequency of FOGI-FLL according to the grid voltage estimation error is proposed, realizing the adaptation of the dynamic and filtering performance of FOGI-FLL, which is called the FOGI-FLL with crossover frequency adaptation (CFAFOGI-FLL). Finally, the experiments are carried out to compare the performances of CFAFOGI-FLL with SOGI-FLL, CSOGI-FLL, and FOGI-FLL. It has been shown by the experimental results that the CFAFOGI-FLL can achieve concurrently better dynamic and steady-state performances than the other compared techniques, and the CFAFOGI-FLL can simultaneously meet the application requirements of fast convergence, high estimation accuracy, and strong filtering capability.