The electronic structures of γ phase copper iodide crystal and the intrinsic point defects associated with iodine and copper have been studied with relativistic density functional theory and embedded cluster method. The simulations for point defects show that the tetrahedron interstitial copper atoms and copper vacancies may lead to the shallow donor and acceptor levels in the energy gap, which is related with the origins of the broad donor-acceptor pair recombination luminescence band 420—430 nm of CuI crystal.