The all-electron full-potential linearized augmented plane-wave method has been used for an ab initio theoretical study of the band structure, the spectral features of the optical susceptibilities, the density of states, and the electron charge density for PbBiBO4. Our calculations show that the valence-band maximum (VBM) and conduction-band minimum (CBM) are located at the center of the Brillouin zone, resulting in a direct energy gap of about 3.2 eV. We have synthesized the PbBiBO4 crystal by employing a conventional solid-state reaction method. The theoretical calculations in this work are based on the structure built from our measured atomic parameters. We should emphasize that the observed experimental X-ray diffraction (XRD) pattern is in good agreement with the theoretical one, confirming that our structural model is valid. Our calculated bond lengths show excellent agreement with the experimental data. This agreement is attributed to our use of full-potential calculations. The spectral features of the optical susceptibilities show a small positive uniaxial anisotropy.