We made model fitting to the mid-to-far infrared spectral energy distributions (SEDs) for different categories of galaxies in the main extragalactic field of the {it Spitzer} First Look Survey with the aid of spectroscopic information from the Sloan Digital Sky Survey. We find that the mid-to-far infrared SEDs of HII galaxies, mixture type galaxies and LINERs can be well fitted by the one-parameter ($alpha$) dust model of Dale et al. plus the 13 Gyr dust-free elliptical galaxy model. The statistics of $alpha$ values indicates that all these galaxies tend to be quiescent, although the HII galaxies are relatively more active than the LINERs. The mid-infrared SEDs of absorption galaxies are well fitted simply by the 13 Gyr dust-free elliptical galaxy template, and the near-to-mid infrared SEDs of QSOs can be represented by AGN NGC 5506.