Context. 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. Although 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 performed wide-field Washington photometry with data obtained with the MOSAIC II camera at the 4m-Blanco telescope (CTIO, Chile). Results. The GCS is very poor with SN ≈ 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 extrordinarily poor GCS of NGC 7507, a massive elliptical galaxy, is an illustration of how important the environmental conditions are for producing rich GCSs.