Star-forming galaxies are huge reservoirs of cosmic rays (CRs) and these CRs convert a significant fraction of their energy into $gamma$-rays by colliding with the interstellar medium (ISM). Several nearby star-forming galaxies have been detected in GeV-TeV $gamma$-rays. It is also found that the $gamma$-ray luminosities in 0.1-100 GeV correlate well with indicators of star formation rates of the galaxies, such as the total infrared (IR) luminosity. In this paper, we report a systematic search for possible $gamma$-ray emission from galaxies in the IRAS Revised Bright Galaxies Sample, using 11.4 years of $gamma$-ray data taken by the Fermi Large Area Telescope (LAT). Two new galaxies, M33 and Arp 299, are detected significantly. The two galaxies are consistent with the empirical correlation between the $gamma$-ray luminosity and total infrared luminosity, suggesting that their $gamma$-ray emissions should mainly originate from CRs interacting with ISM. Nevertheless, there is a tentative evidence that the flux of the $gamma$-ray emission from Arp~299 is variable. If the variability is true, part of the emission from Arp 299 should originate from the obscured AGN in this interacting galaxy system. In addition, we find that the $gamma$-ray excess from M33 is located at the northeast region of the galaxy, where a supergiant H II region, NGC604, resides. This indicates that some bright star-forming regions in spiral galaxies could play a dominant role in the galaxy in producing $gamma$-ray emission.