The detection of transient signal using wavelet transform (WT) has been studied recently. A new method for detection of transient signals with unknown waveforms and arrival times is proposed. The Mexican hat function is chosen as basic wavelet，and combining with the prior information of transient signal，the values of dilation and translation parameters are selected appropriately. As a result transients whose waveforms partially overlap in time at a very low signal-to-noise ratio can be recognized in the WT domain. Using Monte-Carlo simulation，the structure of the proposed detector is discussed and its performance is evaluated.