In this paper, we proposed a distributed stress sensor based on white light interferometer. The measurement including two steps: firstly, the moveable mirror of Michelson interferometer scans to detect the interferogram, and the position of dynamic stress can be obtained from the interferogram. Secondly, the moveable mirror of Michelson interferometer adjusted to compensate the optical path difference generated in the polarization maintaining fiber, and the photodiode detect the interference intensity. By applying wavelet transform to the detect signal, the frequency of dynamic stress can be demodulate. In our experiments, the measurement errors for 100 Hz and 1 kHz sinusoidal stress are 0.26 Hz and 0.3 Hz, respectively. And 20 Hz - 60 Hz chirp signal is also measured successfully. In the end, the harmonics in the time frequency distribution image and the factors resulting in the measurement error are discussed in detail.