The geometrical structure of clean ZnO(0001) surface and B/ZnO(0001) adsorption system are optimized by using the ultra-soft pseudopotential method of total-energy plane wave based on the density functional theory. Adsorption energy, band structure, density of states and optical properties are calculated and discussed in detail. The results reveal that the T4 site is the most stable adsorption site of ZnO(0001) surface. After a B atom is adsorbed on T4 site, the surface band gap narrows down and the surface state changes a lot, the n-type conduction characteristic is weakened. As for the optical properties, we can find that the absorbing ability of ZnO(0001) surface to ultraviolet light is obviously enhanced after the B atom has been adsorbed on the T4 site of ZnO(0001) surface.