We have performed a systematic study resulting in detailed information on the structural, electronic and optical properties of the cubic (Pm3¯m) and tetragonal (P4mm) phases of PbTiO3applying the GGA/PBE approximation with and without the Hubbard U potential correction. Through the variation in Hubbard potential values, we establish band gap predictions for the tetragonal phase of PbTiO3that are in rather good agreement with experimental data. Furthermore, the bond lengths for both phases of PbTiO3were assessed with experimental measurements, confirming the validity of our model, while chemical bond analysis highlights the covalent nature of the Ti–O and Pb–O bonds. In addition, the study of the optical properties of the two phases of PbTiO3, by applying Hubbard’ U potential, corrects the systematic inaccuracy of the GGA approximation, as well as validating the electronic analysis and offering excellent concordance with the experimental results. Therefore, our results underline that the GGA/PBE approximation with the Hubbard U potential correction could be an effective method for obtaining reliable band gap predictions with moderate computational cost. Therefore, these findings will enable theorists to make use of the precise values of these two phases’ gap energies to enhance PbTiO3’s performance for new applications.