CoRoT-21, a F8IV star of magnitude V = 16 mag, was observed by the space telescope CoRoT during the Long Run 01 (LRa01) in the first winter field (constellation Monoceros) from October 2007 to March 2008. Transits were discovered during the light curve processing. Radial velocity follow-up observations, however, were performed mainly by the 10-m Keck telescope in January 2010. The companion CoRoT-21b is a Jupiter-like planet of 2.26 ± 0.33 Jupiter masses and 1.30 ± 0.14 Jupiter radii in an circular orbit of semi-major axis 0.0417 ± 0.0011 AU and an orbital period of 2.72474 ± 0.00014 days. The planetary bulk density is (1.36 ± 0.48) ×103 kg m−3, very similar to the bulk density of Jupiter, and follows an M1/3 − R relation like Jupiter. The F8IV star is a sub-giant star of 1.29 ± 0.09 solar masses and 1.95 ± 0.2 solar radii. The star and the planet exchange extreme tidal forces that will lead to orbital decay and extreme spin-up of the stellar rotation within 800 Myr if the stellar dissipation is Q∗/k2∗ ≤ 107.