The spectra picture of infrared spectra in entire spectrum band can be obtained with the Fourier transform infrared spectroscopy, but sometimes only some one of the spectrums is concerned. Therefore, we need to do some spectrum thinning. The method of Chirp_z transform was used in infrared spectrum thinning, which makes the local ranges of the spectra thinned, and some of these local ranges of infrared spectra pictures were enlarged effectively. This method could realize thinning of the infrared spectra picture in any kinds of band without changing amount of the sampling points. Because the sampling resolution of these local ranges was improved, the higher precision of infrared spectra pictures could be acquired. Both the theoretical analysis and experimental results show that the method of Chirp_z transform has characteristics of high accuracy, high speed and strong flexibility, so it can be widely applied in lots of engineering projects.