Abstract We report the discovery of NGTS-21b , a massive hot Jupiter orbiting a low-mass star as part of the Next Generation Transit Survey (NGTS). The planet has a mass and radius of 2.36 ± 0.21 MJ and 1.33 ± 0.03 RJ, and an orbital period of 1.543 days. The host is a K3V (Teff = 4660 ± 41 K) metal-poor ([Fe/H] = −0.26 ± 0.07 dex) dwarf star with a mass and radius of 0.72 ± 0.04 M⊙ and 0.86 ± 0.04 R⊙. Its age and rotation period of $10.02^{+3.29}_{-7.30}$ Gyr and 17.88 ± 0.08 d respectively, are in accordance with the observed moderately low stellar activity level. When comparing NGTS-21b with currently known transiting hot Jupiters with similar equilibrium temperatures, it is found to have one of the largest measured radii despite its large mass. Inflation-free planetary structure models suggest the planet’s atmosphere is inflated by $\sim 21\%$, while inflationary models predict a radius consistent with observations, thus pointing to stellar irradiation as the probable origin of NGTS-21b’s radius inflation. Additionally, NGTS-21b’s bulk density (1.25 ± 0.15 g/cm3) is also amongst the largest within the population of metal-poor giant hosts ([Fe/H] < 0.0), helping to reveal a falling upper boundary in metallicity-planet density parameter space that is in concordance with core accretion formation models. The discovery of rare planetary systems such as NGTS-21 greatly contributes towards better constraints being placed on the formation and evolution mechanisms of massive planets orbiting low-mass stars.