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 ∼5.64σ detection, named Fermi J1242.5+3236, which has an offset of about 0.º0996 from a nearby star-forming galaxy NGC 4631. When using the 12 yr' data, the detection significance of Fermi J1242.5+3236 is about 4.72σ. 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 ± 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.