In 2008 he tied for 1st–8th with Nigel Short, Vadim Milov, Aleksej Aleksandrov, Tamaz Gelashvili, Alexander Lastin, Gadir Guseinov and Farid Abbasov in the President's Cup in Baku. Jobava won the silver medal in the European Individual Championship 2010, held in Rijeka. In August 2011 he tied for 1st–2nd with Hrant Melkumyan in the Lake Sevan tournament in Martuni and won the event on tie-break. In December 2011 he won the 32nd Edoardo Crespi Trophy in Milan with 8½/9, finishing two points ahead of second placed Vladimir Malaniuk. In the same month Jobava won the European Rapid Chess Championship in Warsaw ahead of 746 players.