In this paper we report on the third soft gamma-ray source catalog obtained with the IBIS/ISGRI gamma-ray imager on board the INTEGRAL satellite. The scientific dataset is based on more than 40 Ms of high quality observations performed during the first three and a half years of Core Program and public IBIS/ISGRI observations. Compared to previous IBIS/ISGRI surveys, this catalog includes a substantially increased coverage of extragalactic fields, and comprises more than 400 high-energy sources detected in the energy range 17-100 keV, including both transients and faint persistent objects which can only be revealed with longer exposure times.