Context : The CoRoT mission , a pioneer in exoplanet searches from space , has completed its first 150 days of continuous observations of \sim 12 000 stars in the galactic plane . An analysis of the raw data identifies the most promising candidates and triggers the ground-based follow-up . Aims : We report on the discovery of the transiting planet CoRoT-Exo-2b , with a period of 1.743 days , and characterize its main parameters . Methods : We filter the CoRoT raw light curve of cosmic impacts , orbital residuals , and low frequency signals from the star . The folded light curve of 78 transits is fitted to a model to obtain the main parameters . Radial velocity data obtained with the SOPHIE , CORALIE and HARPS spectrographs are combined to characterize the system . The 2.5 min binned phase-folded light curve is affected by the effect of sucessive occultations of stellar active regions by the planet , and the dispersion in the out of transit part reaches a level of 1.09 \times 10 ^ { -4 } in flux units . Results : We derive a radius for the planet of 1.465 \pm 0.029 R _ { Jup } and a mass of 3.31 \pm 0.16 M _ { Jup } , corresponding to a density of 1.31 \pm 0.04 g/cm ^ { 3 } . The large radius of CoRoT-Exo-2b can not be explained by current models of evolution of irradiated planets . Conclusions :