Massive galaxies are thought to form in two phases: an initial collapse of gas and giant burst of central star formation, followed by the later accretion of material that builds up their stellar and dark-matter haloes. The systems of globular clusters within such galaxies are believed to form in a similar manner. The initial central burst forms metal-rich (spectrally red) clusters, whereas more metal-poor (spectrally blue) clusters are brought in by the later accretion of less-massive satellites. This formation process is thought to result in the multimodal optical colour distributions that are seen in the globular cluster systems of massive galaxies. Here we report optical observations of the massive relic-galaxy candidate NGC 1277—a nearby, un-evolved example of a high-redshift ‘red nugget’ galaxy. We find that the optical colour distribution of the cluster system of NGC 1277 is unimodal and entirely red. This finding is in strong contrast to other galaxies of similar and larger stellar mass, the cluster systems of which always exhibit (and are generally dominated by) blue clusters. We argue that the colour distribution of the cluster system of NGC 1277 indicates that the galaxy has undergone little (if any) mass accretion after its initial collapse, and use simulations of possible merger histories to show that the stellar mass due to accretion is probably at most ten per cent of the total stellar mass of the galaxy. These results confirm that NGC 1277 is a genuine relic galaxy and demonstrate that blue clusters constitute an accreted population in present-day massive galaxies.