Based on the concentration of no-relaxed oxygen deficient center obtained from experiments and the density of states of conduction band electrons calculated by the first-principles, the 5.0 eV linear absorption coefficient of fused silica is presented. The calculated result is coincident with experiments very well, which supports the proposal that no-relaxed oxygen-deficient center is the defect precursors of 5.0 eV absorption band in fused silica.