  We present a new theoretical calculation of the contribution to the
extragalactic gamma-ray background radiation (EGRB) from star-forming galaxies,
based on a state-of-the-art model of hierarchical galaxy formation that is in
quantitative agreement with a variety of observations of local and
high-redshift galaxies. Gamma-ray luminosity ($L_\gamma$) and spectrum of
galaxies are related to star formation rate ($\psi$), gas mass ($M_gas$), and
star formation mode (quiescent or starburst) of model galaxies using latest
observed data of nearby galaxies. We try the two limiting cases about gamma-ray
production: the escape limit ($L_\gamma \propto \psi M_gas$) and the
calorimetric limit ($L_\gamma \propto \psi$), and our standard model predicts 7
and 4% contribution from star-forming galaxies to the total EGRB flux
(including bright resolved sources) recently reported by the Fermi Gamma-Ray
Space Telescope. Systematic uncertainties do not allow us to determine the EGRB
flux better than by a factor of ~2. The predicted number of nearby galaxies
detectable by Fermi is consistent with the observation. Intergalactic
absorption by pair-production attenuates the EGRB flux only by a modest factor
of ~1.3 at the highest Fermi energy band, and the reprocessed cascade emission
does not significantly alter EGRB at lower photon energies. The sum of the
known contributions from AGNs and star-forming galaxies can explain a large
part of EGRB, with a remarkable agreement between the predicted model spectrum
and observation.
