Abstract We take advantage of the statistical power of the large-volume dark-matter-only Millennium simulation (MS), combined with a sophisticated semi-analytic galaxy formation model, to explore whether the recently reported z = 3.7 quiescent galaxy ZF-COSMOS-20115 (ZF) can be accommodated in current galaxy formation models. In our model, a population of quiescent galaxies with stellar masses and star formation rates comparable to those of ZF naturally emerges at redshifts z < 4. There are two and five ZF analogues at the redshifts 3.86 and 3.58, respectively, in the MS volume. We demonstrate that, while the z > 3.5 massive QGs are rare (about 2 per cent of the galaxies with the similar stellar masses), the existing AGN feedback model implemented in the semi-analytic galaxy formation model can successfully explain the formation of the high-redshift QGs as it does on their lower redshift counterparts.