The classification of celestial spectra is one of the important contents of astronomical research. The key is to select and extract the most effective feature for classification from spectra data. In this paper, we propose a new feature extraction method for astronomical spectra based on two-dimensional Fourier spectrum image, and apply the method to the classification study of LAMOST (the Large Sky Area Multi-Object Fiber Spectroscopic Telescope) stellar spectral data. The spectra data are from LAMOST Data Release 5 (DR5). We select 30000 F, G, and K types of spectra data. The short-time Fourier transform (STFT) is used to transform the one-dimensional spectra data into two-dimensional Fourier spectrum images. We classify and test these two-dimensional Fourier spectrum images with a module based on deep convolutional network, and the classification accuracy rate is 92.90$%$. The experimental result shows that the LAMOST stellar spectra data can be transformed into the two-dimensional Fourier spectrum images by the STFT. These spectral images inform new features, and build a new feature space, which is effective for classification. The method is a fully new attempt in spectra classification, which has certain pioneering significance for the classification and mining of massive celestial spectra.