In recent years, power quality (PQ) disturbance data are increasingly applied to extract useful information about the condition of power systems, such as monitoring incipient equipment failures. A prerequisite for such applications is the ability for a PQ monitor to detect abnormal waveforms. In response to this need, a generic method for waveform abnormality detection is proposed in this paper. The proposed method has two unique features. First, abnormalities are detected by comparing the statistical distributions of waveform variations with and without disturbances. Kullback-Leibler divergence (KLD) is used to assess the difference of the distributions. An abnormality exists if the KLD is larger than a threshold. Second, current waveforms are used for detection since they are more sensitive to equipment conditions. The difficulty to set a proper threshold due to large variations of current values is overcome through the adoption of KLD as the distance measure and a systematic threshold selection scheme. The scheme maximizes the detection probability for a given false alarm probability. Field-measured data and simulated data are applied to verify the effectiveness of the method.