Multicolour images of the starbursting metal poor blue compact galaxy ESO 338-IG04 have been obtained with the Wide Field Planetary Camera 2 on board the Hubble Space Telescope. In the images we find numerous point-like sources concentrated towards the main body of the galaxy, which we identify as globular cluster candidates. We show that these objects are physically associated with the galaxy and that they are spatially extended. Given their high intrinsic luminosities, these objects cannot be individual stars. Using photometric evolution models we show that the objects constitute a rich population of massive star clusters with ages ranging from a few Myr to 10Gyr, and masses ranging from 10^4^ to more than 10^7^M_{sun}_. There are peaks in the age distribution of the clusters: one with objects <=30Myr, one at ~100Myr, one at ~600Myr, one to two at 2.5-5Gyr and one at ~10Gyr. The youngest objects are predominantly found in the crowded starburst region. They have properties which agree with what is expected for young globular clusters, although it cannot be excluded that some of them may be dissolved or disrupted. For objects older than a few times 10Myr, the only plausible explanation is that these are globular clusters. The galaxy presently appears to be involved in a merger, which is the probable cause of the present globular cluster formation. The presence of a numerous intermediate age (2.5 to 5Gyr) population of globular clusters, suggests that a previous merger might have occurred. As the starburst fades, this galaxy will become very rich in globular clusters. Transforming all objects to an age comparable to that of Milky Way globular clusters reveals a luminosity function similar to the Galactic. We suggest that this galaxy is the result of a merger between a dwarf elliptical and a gas rich dwarf. The possibility of dating the globular clusters offers an efficient way of studying the history of violent star formation in this and similar galaxies.