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Wavelet packet transform (WPT) is one of the most powerful tools in the analysis of the nonstationary signals. Shannon wavelet function is the only function that can divide the frequency domain strictly in the single wavelet family, but the time waveform of Shannon wavelet is not compactly supported, so the application of it is limited. In this paper, a kind of optimized Shannon wavelet transform (SWPT) algorithm is proposed. Firstly, the incompactly supported characters is improved in time domain by modification the function's time expression; secondly; the interpolation algorithm in SWPT'S frequency filter is proposed to ameliorate the performance father more; then the fast computation of algorithm using chirp Z transform is implemented, at last the numeric simulation has been given out. The result shows the algorithm improves the performance of the SWPT effectively.