In this paper we report the second soft gamma-ray source catalog obtained with the IBIS/ISGRI gamma-ray imager on board the INTEGRAL satellite. The scientific data set is based on more than 10 Ms of high-quality observations performed during the first 2 years of Core Program and public IBIS/ISGRI observations, and covers ~50% of the whole sky. The main aim of the first survey was to scan systematically, for the first time at energies above 20 keV, the whole Galactic plane to achieve a limiting sensitivity of ~1 mcrab in the central radian. The target of the second year of the INTEGRAL mission lifetime was to expand as much as possible our knowledge of the soft gamma-ray sky, with the same limiting sensitivity, to at least 50% of the whole sky, mainly by including a substantial coverage of extragalactic fields. This catalog comprises more than 200 high-energy sources detected in the energy range 20-100 keV, including new transients not active during the first year of operation, faint persistent objects revealed with longer exposure time, and several Galactic and extragalactic sources in sky regions not observed in the first survey. The mean position error for all the sources detected with significance above 10 ? is ~40", enough to identify most of them with a known X-ray counterpart and to unveil the nature of most of the strongly absorbed ones, even though they are very difficult to detect in X-rays. Based on observations with INTEGRAL, an ESA project with instruments and science data center funded by ESA member states (especially the PI countries: Denmark, France, Germany, Italy, Switzerland, Spain), Czech Republic, and Poland, and with the participation of Russia and the USA.