We present the GALEX NUV (2310 A) and FUV (1530 A) galaxy luminosity functions of the nearby cluster of galaxies A1367 in the magnitude range -20.3< M_AB < -13.3. The luminosity functions are consistent with previous (~ 2 mag shallower) estimates based on the FOCA and FAUST experiments, but display a steeper faint-end slope than the GALEX luminosity function for local field galaxies. Using spectro-photometric optical data we select out 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 LF is entirely due to the contribution at low luminosities (M_AB >-16 mag) of non star-forming, early-type galaxies that are significantly over dense in clusters.