Context: The CoRoT mission, a pioneer in exoplanet searches from space, has completed its first 150 days of continuous observations of ~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 1.09×10-4 in flux units. Results: We derive a radius for the planet of 1.465 ± 0.029 R_Jup and a mass of 3.31 ± 0.16 M_Jup, corresponding to a density of 1.31 ± 0.04 g/cm^3. The large radius of CoRoT-Exo-2b cannot be explained by current models of evolution of irradiated planets. Based on observations obtained with CoRoT, a space project operated by the French Space Agency, CNES, with participation of the Science Programme of ESA, ESTEC/RSSD, Austria, Belgium, Brazil, Germany and Spain; and on observations made with SOPHIE spectrograph at Observatoire de Haute Provence, France (PNP.07 A.MOUT), CORALIE, and HARPS spectrograph at ESO La Silla Observatroy (079.C-0127/F)). Table 2 is only available in electronic form at http://www.aanda.org