First‐principles calculations based on the density functional theory and the generalized gradient approximation were carried out to systematically investigate the electronic structure and linear optical properties of lead tetraborate (PbB4O7; PTB) single crystals. An indirect band gap of 4.34 eV is obtained. The valence band top is at the X‐point and the conduction band is at the Γ‐point. The calculated total and partial densities of states indicate that the top valence band is constructed from O 2p states and the low conduction band mainly consists of Pb 6p states. The optical absorption spectra show several prominent structures but with very small directional anisotropy. PTB crystals have a higher refractive index but a small birefringence. The calculated frequency‐dependent refractive index is in good agreement with experimental data. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)