I present new theoretical modelling to predict high-energy gamma-ray and neutrino luminosity and spectrum of a star-forming galaxy, from the star-formation rate, gas mass, stellar mass, and size. This model fairly well reproduces gamma-ray luminosities of nearby galaxies detected by Fermi. This model is then combined with a model of cosmological galaxy formation to predict the cosmic background flux of gamma-ray and neutrino from star-formation across cosmic time. In our baseline model, star-forming galaxies produce about 20% of the isotropic gamma-ray background, and only 0.5% of the IceCube neutrino diffuse flux. Even with an extremely optimistic model, at most 22% of IceCube neutrinos can be accounted for. These results show that it is difficult to explain majority of the IceCube flux by star-forming galaxies.