A transient displacement interferometer signal processing method based on the continuous wavelet transform (CWT) is proposed. The interference signal is analyzed by CWT, and the frequency and the velocity of the signal can be deduced. One main characteristic of CWT is its adaptive nature for signals with large variations in frequency. In the flexible time window, if the varying central frequency is equal or close to the instantaneous frequency of local signals, the modulus of CWT is maximal, so the local frequency is determined. The processing results of simulated interference signals show that the relative error is less than 3%. Similarly, velocity history can be precisely recovered from signals of fiber displacement interferometer in detonation experiment.