We present a theoretical study of the electronic structure of the wurtzite CuInSb>2b> material. To address reliably some material properties of this new phase we use hybrid density functional theory. Among possible wurtzite polymorphs, we have determined the most stable phase on the basis of total energy minimization. The minimum energy structure exhibits a semiconducting ground state with a band gap of 1.3 eV in excellent agreement with experimental data. We use time-dependent density functional theory to compare the optical response of the chalcopyrite and wurtzite phases and to identify the nature of the optically active transitions in the vicinity of the absorption edge. Our analysis indicates that the wurtzite CuInSb>2b> structure is a suitable material for photovoltaic applications.