ABSTRACT We report the discovery of K2-56b, a high-density sub-Neptune exoplanet, made using photometry from Campaign 4 of the two-wheeled Kepler (K2) mission, ground-based radial velocity (RV) follow-up from HARPS and high-resolution lucky and adaptive optics imaging obtained using AstraLux and MagAO, respectively. The host star is a bright (V = 11.04, Ks = 9.37), slightly metal-poor (Fe/H = −0.15 0.05 dex) solar analogue located at pc from Earth, for which we find a radius of and a mass of . A joint analysis of the K2 photometry and HARPS RVs reveal that the planet is in a 42 day orbit around its host star, has a radius of , and a mass of . Although the data at hand put the planet in the region of the mass-radius diagram where we could expect planets with a pure rock (i.e., magnesium silicate) composition using two-layer models (i.e., between rock/iron and rock/ice compositions), we discuss more realistic three-layer composition models which can explain the high density of the discovered exoplanet. The fact that the planet lies in the boundary between "possibly rocky" and "non-rocky" exoplanets makes it an interesting planet for future RV follow-up.