We explore the age distribution of the globular cluster (GC) system of the nearby elliptical galaxy NGC 5128 using ultraviolet (UV) photometry from GALEX observations, with UV-optical colors used as the age indicator. Most GCs in NGC 5128 follow the general trends of GCs in M31 and the Milky Way in the UV-optical color-color diagram, which indicates that the majority of GCs in NGC 5128 are old similar to the age range of old GCs in M31 and the Milky Way. A large fraction of spectroscopically identified intermediate-age GC (IAGC) candidates with ~3-8 Gyr are not detected in the far-UV (FUV) passband. Considering the nature of intermediate-age populations being faint in the FUV passband, we suggest that many of the spectroscopically identified IAGCs may be truly intermediate in age. This is in contrast to the case of M31 where a large fraction of spectroscopically suggested IAGCs are detected in FUV and therefore may not be genuine IAGCs but rather older GCs with developed blue horizontal branch stars. Our UV photometry strengthens the results previously suggesting the presence of GC and stellar subpopulation with intermediate age in NGC 5128. The existence of IAGCs strongly indicates the occurrence of at least one more major star formation episode after a starburst at high redshift.