We announce the discovery of the transiting planet CoRoT-13b . Ground based follow-up in CFHT and IAC80 confirmed CoRoT ’ s observations . The mass of the planet was measured with the HARPS spectrograph and the properties of the host star were obtained analyzing HIRES spectra from the Keck telescope . It is a hot Jupiter-like planet with an orbital period of 4.04 days , 1.3 Jupiter masses , 0.9 Jupiter radii , and a density of 2.34 g cm ^ { -3 } . It orbits a G0V star with T _ { \mathrm { eff } } = 5 945 K , M _ { * } = 1.09 M _ { \odot } , R _ { * } = 1.01 R _ { \odot } , solar metallicity , a lithium content of +1.45 dex , and an estimated age between 0.12 and 3.15 Gyr . The lithium abundance of the star is consistent with its effective temperature , activity level , and age range derived from the stellar analysis . The density of the planet is extreme for its mass . It implies the existence of an amount of heavy elements with a mass between about 140 and 300 \mathrm { M } _ { \oplus } .