We have performed a first-principles study of the structural, electronic, and optical properties of the cubic state of PbTiO3 by means of the density functional theory full potential linearized augmented plane wave (FP-LAPW) method with the generalized gradient approximation (GGA), Engle-Vosco approximation (EVA), and the local spin density approximation with the Hubbard parameter U (LSDA+U). The calculated electronic structure and charge density yield a band gap of 3.3 eV at the X point in the Brillouin zone. The theoretical optical properties and electron energy loss spectrum yield a static refractive index of 2.83 and plasmon energy of 24 eV for the cubic phase of PbTiO3.