We present ultraviolet (UV) photometry of M31 globular clusters (GCs) found in 23 Galaxy Evolution Explorer (GALEX) images covering the entirety of M31. We detect 485 and 273 GCs (and GC candidates) in the near-ultraviolet (NUV) and far-ultraviolet (FUV), respectively. The UV properties of GCs have been analyzed using various combinations of UV-optical and optical-optical colors. Comparing M31 data with those of Galactic GCs in the UV with the aid of population models, we find that the age ranges of old GCs in M31 and the Galactic halo are similar. Three metal-rich ([Fe/H]>-1) GCs in M31 produce significant FUV flux making their FUV-V colors unusually blue for their metallicities. These are thought to be analogs of the two peculiar Galactic GCs, NGC 6388 and NGC 6441, with extended blue HB stars. We detect 12 (10) intermediate-age GC candidates in NUV (FUV) identified by previous spectroscopic observations. On the basis of comparing our UV photometry to population models, we suggest that some of spectroscopically identified intermediate-age GCs may not be truly intermediate in age, but rather older GCs that possess developed HB stars which contribute to enhanced UV flux as well as Balmer lines.