Using the plane-wave ultrasoft pseudopotential technique based on the first-principles density functional theory (DFT), we have studied the structural, electronic, chemical bonding, and optical properties of tetragonal PbMoO4. The obtained structural parameters are in good agreement with experiments. Band structure, density of states, and chemical bonding are calculated and shown. It is found that tetragonal PbMoO4 is an indirect band gap. The dielectric function, refractive index, extinction coefficient, reflectivity, absorption coefficient, loss function, and conductivity function are calculated for radiation up to 20 eV.