Gaussian pulse shaping filter of exponential decay signal based on wavelet analysis can be more described by using linear combination of both Gaussian function and its first order derivative. On the basis of the recursive approximate algorithm of Gaussian function and its derivative, the recursive approximate algorithm of Gaussian pulse shaping of exponential decay signal based on wavelet analysis is studied. The experiment results with simulating and sampling signals show that the recursive approximate Gaussian pulse shaping is well accorded with the direct convolution of the Gaussian pulse shaping. The characteristic of the Gaussian pulse shaping based on wavelet analysis is well exhibited by the recursive approximate Gaussian pulse shaping. The obtained result can serve as the digital algorithmic base for studying the realization of the Gaussian pulse shaping in digital chip.