Using density-functional theory, we perform an ab initio study of PbSiO3 alamosite. The lattice parameters and the internal atomic positions are found within 2% of the experimental data. We compute the electronic structure, analyze the valence bands, and identify three groups of electronic bands. The dispersion is very weak, even along the SiO4 tetrahedra chain direction. The analysis of Bader atomic charges allows us to distinguish different types of oxygen atoms. Then, using density-functional perturbation theory, we obtain the electronic dielectric tensor and the Born effective charge tensors of each atomic species. Lead and oxygen atoms are the main polarizable entities, and Born effective charge tensors of some of the oxygen atoms are quite anisotropic.