We present the Galaxy Evolution Exlorer (GALEX) near-ultraviolet (2310 Å) and far-ultraviolet (1530 Å) galaxy luminosity functions of the nearby cluster of galaxies A1367 in the magnitude range -20.3 ≤ MAB ≤ -13.3. The luminosity functions are consistent with previous (~2 mag shallower) estimates based on the FOCA and FAUST experiments, but they display a steeper faint-end slope than the GALEX luminosity function for local field galaxies. Using spectrophotometric optical data, we select star-forming systems from quiescent galaxies and study their separate contributions to the cluster luminosity function. We find that the UV luminosity function of cluster star-forming galaxies is consistent with the field. The difference between the cluster and field luminosity functions is entirely due to the contribution at low luminosities (MAB > -16 mag) of non-star-forming, early-type galaxies that are significantly overdense in clusters.