Oxygen-ion conduction in apatite-type lanthanum silicate, La9.33+0.67x (SiO4)6O2+x (x = 1), has theoretically been analyzed in a first-principles manner followed by the nudged elastic band method and the kinetic Monte Carlo method. Unlike the conventional cooperative interstitialcy mechanism along the single O4 columns, diffusing interstitial oxygen ions are frequently blocked by adjacent interstitial oxygen ions (Oint ions), leading to the strongly-correlated diffusivity and conductivity of oxygen ions in the case of chemical compositions with large x values. The getting-out mechanism from the O4 column is of importance in the long-range conduction, which temporarily transfers a part of Oint ions out of the columns to relax the blocking effect. The getting-out mechanism plays a key role also in the conduction perpendicular to the c axis (in the ab plane).