Neptune-sized planets exhibit a wide range of compositions and densities, depending on factors related to their formation and evolution history, such as the distance from their host stars and atmospheric escape processes. They can vary from relatively low-density planets with thick hydrogen–helium atmospheres1,2 to higher-density planets with a substantial amount of water or a rocky interior with a thinner atmosphere, such as HD 95338 b (ref. 3), TOI-849 b (ref. 4) and TOI-2196 b (ref. 5). The discovery of exoplanets in the hot-Neptune desert6, a region close to the host stars with a deficit of Neptune-sized planets, provides insights into the formation and evolution of planetary systems, including the existence of this region itself. Here we show observations of the transiting planet TOI-1853 b, which has a radius of 3.46 ± 0.08 Earth radii and orbits a dwarf star every 1.24 days. This planet has a mass of 73.2 ± 2.7 Earth masses, almost twice that of any other Neptune-sized planet known so far, and a density of 9.7 ± 0.8 grams per cubic centimetre. These values place TOI-1853 b in the middle of the Neptunian desert and imply that heavy elements dominate its mass. The properties of TOI-1853 b present a puzzle for conventional theories of planetary formation and evolution, and could be the result of several proto-planet collisions or the final state of an initially high-eccentricity planet that migrated closer to its parent star. Observations of the super-massive Neptune-sized transiting planet TOI-1853 b show a mass almost twice that of any other Neptune-sized planet known so far and a bulk density implying that heavy elements dominate its mass.