Here we report the synthesis and discovery of superconductivity in a novel ternary iridium-arsenide compound BaIr2As2. The polycrystalline BaIr2As2 sample was synthesized by a high temperature and high pressure method. Crystal structural analysis indicates that BaIr2As2 crystallizes in the ThCr2Si2-type layered tetragonal structure with space group I4/mmm (No. 139), and the lattice parameters were refined to be a = 4.052(9) {AA} and c = 12.787(8) {AA}. By the electrical resistivity and magnetic susceptibility measurements we found type-II superconductivity in the new BaIr2As2 compound with a Tc (critical temperature) of 2.45 K, and an upper critical field u0Hc2(0) about 0.2 T. Low temperature specific heat measurements gave a Debye temperature about 202 K and a distinct specific jump with delta Ce/{gamma}Tc = 1.36, which is close to the value of BCS weak coupling limit and confirms the bulk superconductivity in this new BaIr2As2 compound.