Gaussian pulse shaping of exponential decay signal based on wavelet analysis is reported. The peak height of Gaussian shaping signal represents the energy of radiation particle and the peak position represents the time of radiation event occurring, respectively. The experimental results with simulating and sampling signals show that the exponential decay signal has been shaped into Gaussian signal, which indicates that Gaussian pulse shaping based on wavelet analysis is valid. The result may serve as the theoretical basic for studying digital realization of Gaussian pulse shaping.