Aims. In the context of the search for extrasolar planets and brown dwarfs around early-type main-sequence stars we present the detection of a giant planet around the young F-type star HD 113337. We estimated the age of the system to be 150 \hbox{$_{-50}^{+100}$}+100-50 Myr. Interestingly, an infrared excess attributed to a cold debris disk was previously detected around this star. Methods. We used the SOPHIE spectrograph on the 1.93 m telescope at Observatoire de Haute-Provence to obtain ~300 spectra over six years. We used our tool dedicated to the spectra analysis of A and F stars to derive the radial velocity variations. Results. The data reveal a period of \hbox{$324.0^{+1.7}_{-3.3}$}324.0-3.3+1.7 days that we attribute to a giant planet with a minimum mass of 2.83 ± 0.24 MJup in an eccentric orbit with e = 0.46 ± 0.04. A long-term quadratic drift, which we assign to be probably of stellar origin, is superimposed on the Keplerian solution.