To improve the ultraviolet-damage threshold of the fused-quartz optics in the high-power laser facility, damage mechanism of the fused-quartz optics is investigated with the beam-transmission theory by analyzing the microscopic configuration of damage which was irradiated hundreds of times with a high-power 351 nm laser. The results show that the subsurface scratch is the mostly important factor that induces ultraviolet damage. It can lower initial damage threshold of fused-quartz optics by several times, even tens of times. The effect of beam diffraction accelerates the damage. Small-scale nonlinear self-focusing is the mostly important body damage mechanism of lens with 40 mm thickness at the end of the final optics. Modulation in the near field of the beam results in high intensity in local area and raises the risk of optics damage. Therefore, it is necessary to reform the processing technologies for the improvement of the damage threshold in the ultraviolet waveband.