The method for analyzing signal singularity using wavelet transform(WT), of which the prime function is smooth, is based on the relation of singularity and Lipschitz regularity of signals. The principle of the method is that the wavelet transform Wψ(a,t) of a signal equals to the first derivative of its smoothed version, s(t)θa(t), so that the maximum points of derivalive must occur at the sharply change points of the signal. Therefore, the maximum points of s(t)θa(t) must result in the singularity points of s(t). The simulation shows that the method can detect the singularity points of signals indeed.