Aims: We report the discovery of CoRoT-16b, a low density hot jupiter that orbits a faint G5V star (mV = 15.63) in 5.3523 ± 0.0002 days with slight eccentricity. A fit of the data with no a priori assumptions on the orbit leads to an eccentricity of 0.33 ± 0.1. We discuss this value and also derive the mass and radius of the planet. Methods: We analyse the photometric transit curve of CoRoT-16 given by the CoRoT satellite, and radial velocity data from the HARPS and HIRES spectrometers. A combined analysis using a Markov chain Monte Carlo algorithm is used to get the system parameters. Results: CoRoT-16b is a 0.535 -0.083/+0.085 MJ, 1.17 -0.14/+0.16 RJ hot Jupiter with a density of 0.44 -0.14/+0.21 g cm-3. Despite its short orbital distance (0.0618 ± 0.0015 AU) and the age of the parent star (6.73 ± 2.8 Gyr), the planet orbit exhibits significantly non-zero eccentricity. This is very uncommon for this type of objects as tidal effects tend to circularise the orbit. This value is discussed taking into account the characteristics of the star and the observation accuracy. The CoRoT space mission, launched on December 27, 2006, has been developed and is operated by the CNES with the contribution of Austria, Belgium, Brasil, ESA, Germany, and Spain.Observations made with the HARPS spectrograph at ESO La Silla Observatory (HARPS programs 083.C-0186 and 184.C-0639) and the HIRES spectrograph at the Keck Observatory (NASA-Keck programs N035Hr, N143Hr and N095Hr).