A microwave photonic short-time Fourier transform (STFT) system based on stabilized period-one (P1) nonlinear laser dynamics and stimulated Brillouin scattering (SBS) is proposed. By using an optoelectronic feedback loop, the frequency-sweep optical signal generated by the P1 nonlinear laser dynamics is stabilized, which is further used in conjunction with an optical bandpass filter implemented by stimulated Brillouin scattering (SBS) to achieve the frequency-to-time mapping of microwave signals and the final STFT. By comparing the experimental results with and without optoelectronic feedback, it is found that the time-frequency diagram of the signal under test (SUT) obtained by STFT is clearer and more regular, and the frequency of the SUT measured in each frequency-sweep period is more accurate. The mean absolute error is reduced by 50% under the optimal filter bandwidth.