It is spontaneous scattering light that the optical time domain reflector (OTDR) based on Brillouin scattering distributed optical fiber sensor detects, which is very weak, and has a frequency width of several decades megahertz, so it is difficult to perform traditional coherent demodulation. A novel optical coherent detection based on Morlet wavelet transform is presented according to the signal's characteristic. Firstly, the spontaneous Brillouin back-scattering light is coherently detected with the frequency-shifted light modulated by a microwave electric optical modulator as the reference light. Secondly, the detected photocurrent signal is processed with amplitude demodulation by Morlet wavelet transform. Finally, the distributed sensing signal with improved signal-noise ratio is gained. The simulation and experimental results of the detection method are given, and the proposed method can process the Brillouin optical time domain reflector signal quite well. The methods based on Morlet wavelet transform and Hilbert transform respectively are compared, and it is found that the former is better for Brillouin optical time domain reflector.