In this paper a method of recognizing waveform based on the Discrete Wavelet Transform (DWT) presented by us is applied to detecting the K-complex in human's EEG which is a slow wave overridden by fast rhythms (called as spindle). The features of K-complex are extracted in terms of three parameters: the local maxima of the wavelet transform modulus, average slope and the number of DWT coefficients in a wave. The 4th order B-spline wavelet is selected as the wavelet basis. Two channels at different resolutions are used to detect slow wave and sleep spindle contained in the K-complex. According to the principle of the minimum distance classification the classifiers are designed in order to decide the thresholds of recognition criteria. The EEG signal containing K-complexes elicited by sound stimuli is used as pattern to train the classifiers. Compared with traditional method of waveform recognition in time domain, this method has the advantage of automatically classifying duration ranks of various waves with different frequencies. Hence, it specially is suitable to recognition of signals which are the superimposition of waves with different frequencies. The experimental results of detection of K-complexes indicate that the method is effective.