The teleparallel versions of the Einstein and the Landau-Lifshitz energy-momentum complexes of the gravitational field are obtained. By using these complexes, the total energy of the universe, which includes the energy of both the matter and the gravitational fields, is then obtained. It is shown that in the case of a closed universe, the total energy vanishes independently of the pseudotensor used, as well as of the three dimensionless coupling constants of teleparallel gravity.