There is strong evidence that globular cluster systems (GCSs) of massive galaxies are largely assembled by infall/accretion processes. Therefore, we expect the GCSs of isolated elliptical galaxies to be poor. Alhough not completely isolated, NGC 7507 is a massive field elliptical galaxy with an apparently very low dark matter content. Aims: We determine the richness, the colour distribution, and the structural properties of the GCS of NGC 7507. Methods: We perform wide-field Washington photometry with data obtained with the MOSAIC II camera at the 4m-Blanco telescope, CTIO. Results: The GCS is very poor with S_N ~ 0.6. We identify three subpopulations with peaks at (C-T1) colours of 1.21, 1.42, and 1.72. The bluest population may represent the old, metal-poor component. This interpretation is supported by its shallow density profile. The red population is more concentrated, resembling the galaxy light. The intermediate-colour population is strongly peaked in colour and we interpret this population as the signature of a starburst, whose age depends on the metallicity, but should be quite old, since no signatures of a merger are identifiable. In addition, we find a main sequence in the stellar foreground population, which we attribute to the Sagittarius dwarf tidal stream. Conclusions: The extraordinarily poor GCS of NGC 7507, a massive elliptical galaxy, is an illustration of how important the environmental conditions are for producing rich GCSs.