We have investigated the effects of sputtering Ar gas pressure on magnetic anisotropy of Co/Pt multilayers, where sputtering Ar gas pressure was varied from 2 to 20 mTorr. The surface and volume anisotropies were found to be strongly dependent on sputtering Ar gas pressure. In particular, the surface anisotropy exhibited more than fourfold enhancement as Ar pressure was decreased from 20 to 5 mTorr. We have found that the surface anisotropy was closely correlated with the low-angle x-ray diffraction intensity. We believe that these results are mainly ascribed to the variation of microstructure in the Co/Pt multilayer thin films with sputtering Ar gas pressure.