Characteristics in pulse wave signals (PWSs) include the information of physiology and pathology of human cardiovascular system. Therefore, identification of characteristic points in PWSs plays a significant role in analyzing human cardiovascular system. Particularly, the characteristic points show personal dependent features and are easy to be affected. Acquiring a signal with high signal-to-noise ratio (SNR) and integrity is fundamentally important to precisely identify the characteristic points. Based on the mathematical morphology theory, we design a combined filter, which can effectively suppress the baseline drift and remove the high-frequency noise simultaneously, to preprocess the PWSs. Furthermore, the characteristic points of the preprocessed signal are extracted according to its position relations with the zero-crossing points of wavelet coefficients of the signal. In addition, the differential method is adopted to calibrate the position offset of characteristic points caused by the wavelet transform. We investigated four typical PWSs reconstructed by three Gaussian functions with tunable parameters. The numerical results suggested that the proposed method could identify the characteristic points of PWSs accurately.