The demodulation accuracy of the traditional microwave photonic filtering interrogation technique based on the frequency-time transform is limited by the radio frequency (RF) response measurement bandwidth when it is applied to multi-points or quasi-distributed sensing systems. By the idea of the zoom fast Fourier transform (Zoom-FFT) of the spectrum refinement algorithm, the expression of time-domain refinement is derived, which effectively solves the problem of mutual restriction between RF response measurement bandwidth, demodulation rate, and demodulation accuracy. Compared with the direct and zero-padding inverse discrete Fourier transforms, the proposed algorithm can greatly reduce the requirements for the RF response measurement bandwidth and the computation load of frequency-time transform under the same time-domain resolution, and the demodulation rate is effectively improved. In the verification experiment, a multi-point sensing system containing five fiber Bragg gratings (FBGs) is constructed. The test results reveal that under the same time-domain resolution, the calculated sampling points and time consumption of the proposed algorithm are reduced to 1/200 and 10/145 of the results of the zero-padding algorithm, respectively; for a given 5 GHz sweep-frequency bandwidth, the time-domain resolution in sub-picosecond level can be achieved when the number of sampling points is greater than 1000, which corresponds to the picometer-level wavelength demodulation precision of FBGs.