We selected a sample of luminous infrared galaxies by cross-identification of the Faint Source Catalogue (FSC) and Point Source Catalogue (PSC) of the IRAS Survey with the Second Data Release of the SDSS. The size of our sample is 1267 for FSC and 427 for PSC by using the 2σ significance level cross-section. The ``likelihood ratio" method is used to estimate the individual's reliability and for defining two more reliable subsamples (908 for FSC and 356 for PSC). A catalog of infrared, optical and radio data is compiled and will be used in further work. Some statistical results show that luminous infrared galaxies are quite different from ultra-luminous infrared galaxies. The AGN fractions of galaxies at different infrared luminosities and the radio–infrared correlations are consistent with the previous studies.