In recent years, a new mathematical technique called wavelet transform (WT) has been developed and adopted for signal processing in analytical chemistry owing to its efficiency, more number of basis functions available, and higher speed in data treatment compared to fast Fourier transform (FFT). In this paper, the fast wavelet transform (FWT) and its derivative, wavelet packet transform (WPT), were applied to compress infrared (IR) spectrum for storage and spectral searching. In WT treatment, the number of data to be processed has to be 2P with P being any integer. In this work, we proposed the coefficient position retaining (CPR) method to handle data with length of odd number. The performance of the two proposed WT methods in data compression and spectral library searching are compared with that of the FFT method. The results indicated that our proposed WT methods works better than FFT in compression of IR spectra and spectral library searching.