  Based on the first 13.4 yr of Fermi science data in the energy range from 300
MeV to 500 GeV, we discovered a bright GeV gamma-ray source with a $\sim$5.64
$\sigma$ detection, named Fermi J1242.5+3236, which has an offset of about
0fdg0996 from a nearby star-forming galaxy NGC 4631. When using the 12-yr data,
the detection significance of Fermi J1242.5+3236 is about 4.72 $\sigma$. Fermi
J1242.5+3236 is a steady point source without significant temporal variability
and has a hard gamma-ray photon index of about -1.60 $\pm$0.24. The spatial
offset and the hard gamma-ray spectrum disfavor this source as the diffuse
gamma-ray emission from this galaxy. This new source might have a possible
origin of an unidentified background blazar, which is more likely a
high-synchrotron-peaked blazar for its hard gamma-ray photon index. A follow-up
optical observation would help distinguish origin of Fermi J1242.5+3236.
