A time-varying microwave photonic filter (TV-MPF) based on stimulated Brillouin scattering (SBS) is proposed and utilized to suppress the in-band noise of broadband arbitrary microwave waveforms, thereby improving the signal-to-noise ratio (SNR). The filter-controlling signal is designed according to the signal to be filtered and drives the TV-MPF so that the passband of the filter is always aligned with the frequencies of the signal to be filtered. By continuously tracking the signal spectral component, the TV-MPF only retains the spectral components of the signal and filters out the noise other than the spectral component of the signal at the current time, so as to improve the in-band SNR of the signal to be filtered. An experiment is performed. A variety of signals with different formats and in-band SNRs are used to test the noise suppression capability of the TV-MPF, and the waveform mean-square error is calculated to quantify the improvement of the signal, demonstrating the excellent adaptability of the proposed TV-MPF to different kinds of signals.