We present a new theoretical modeling to predict luminosity and spectrum of gamma-ray and neutrino emission of a star-forming galaxy, from star formation rate (ψ), gas mass (M_ gas), stellar mass, and disk size, taking into account production, propagation and interactions of cosmic rays. The model reproduces the observed gamma-ray luminosities of nearby galaxies detected by Fermi better than the simple power-law models as a function of ψ or ψ M_ gas. Then this model is used to predict the

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... background flux of gamma-ray and neutrinos from star-forming galaxies, by using a semi-analytical model of cosmological galaxy formation that reproduces many observed quantities of local and high-redshift galaxies. Calibration of the model using gamma-ray luminosities of nearby galaxies allows us to make a more reliable prediction than previous studies. In our baseline model star-forming galaxies produce about 20 Fermi, and only 0.5 a hard injection cosmic-ray spectral index of 2.0 for all galaxies, at most 22 of IceCube neutrinos can be accounted for. These results indicate that it is difficult to explain most of IceCube neutrinos by star-forming galaxies, without violating the gamma-ray constraints from nearby galaxies.