Context : The space telescope CoRoT searches for transiting extrasolar planets by continuously monitoring the optical flux of thousands of stars in several fields of view . Aims : We report the discovery of CoRoT-10b , a giant planet on a highly eccentric orbit ( e = 0.53 \pm 0.04 ) revolving in 13.24 days around a faint ( V=15.22 ) metal-rich K1V star . Methods : We use CoRoT photometry , radial velocity observations taken with the HARPS spectrograph , and UVES spectra of the parent star to derive the orbital , stellar and planetary parameters . Results : We derive a radius of the planet of 0.97 \pm 0.07 ~ { } \hbox { $ \mathrm { R } _ { Jup } $ } and a mass of 2.75 \pm 0.16 ~ { } \hbox { $ \mathrm { M } _ { Jup } $ } . The bulk density , \rho _ { p } = 3.70 \pm 0.83 ~ { } { g cm ^ { -3 } } , is \sim 2.8 that of Jupiter . The core of CoRoT-10b could contain up to 240 M _ { \oplus } of heavy elements . Moving along its eccentric orbit , the planet experiences a 10.6-fold variation in insolation . Owing to the long circularisation time , \tau _ { circ } > 7 Â Gyr , a resonant perturber is not required to excite and maintain the high eccentricity of CoRoT-10b . Conclusions :