First-principles calculations of the electronic, optical, and lattice vibrational properties of AgSbTe2 were performed with the generalized gradient approximation (GGA) and the screened-exchange local-density approximation (sx-LDA) method, which successfully corrects the band-gap problem found with GGA. We find a vanishing density of states at the Fermi level, which is consistent with the semiconducting behavior of AgSbTe2. Various optical properties, including the dielectric function, absorption coefficient, and refractive index, as functions of the photon energy are also calculated with the sx-LDA and are found to be in good agreement with experiments. Phonon spectra obtained by the cumulant force constant method show that the optic modes of AgSbTe2 are very low in frequency and should scatter strongly with acoustic modes during heat transport. The calculated specific-heat curve is in general agreement with experiment. Ag/Sb disorder is expected to have a small effect on the electrical transport but may introduce strong phonon scattering due to the large force constant disorder. The scattering of acoustic phonons by optic modes and the possible Ag/Sb disorder may explain the extremely low lattice thermal conductivity of AgSbTe2.