Olivine is a major component of the mantle of differentiated bodies, including Earth. Howardite, eucrite and diogenite (HED) meteorites represent regolith, basaltic-crust, lower-crust and possibly ultramafic-mantle samples of asteroid Vesta, which is the lone surviving, large, differentiated, basaltic rocky protoplanet in the Solar System. Only a few of these meteorites, the orthopyroxene-rich diogenites, contain olivine, typically with a concentration of less than 25 per cent by volume. Olivine was tentatively identified on Vesta, on the basis of spectral and colour data, but other observations did not confirm its presence. Here we report that olivine is indeed present locally on Vesta's surface but that, unexpectedly, it has not been found within the deep, south-pole basins, which are thought to be excavated mantle rocks. Instead, it occurs as near-surface materials in the northern hemisphere. Unlike the meteorites, the olivine-rich (more than 50 per cent by volume) material is not associated with diogenite but seems to be mixed with howardite, the most common surface material. Olivine is exposed in crater walls and in ejecta scattered diffusely over a broad area. The size of the olivine exposures and the absence of associated diogenite favour a mantle source, but the exposures are located far from the deep impact basins. The amount and distribution of observed olivine-rich material suggest a complex evolutionary history for Vesta.