First-principles plane-wave pseudopotential calculations were performed to study the energetics and the geometical structures of intrinsic vacancies and interstitials on the anatase TiO2 (101) crystal surface. Firstly，we analyzed the effects of point defects on the geometrical structures. For the O vacancy，all the nearest-neighbor Ti atoms move away from the vacancy toward the other O neighborhood. As Ti1 or Ti2 is missing here，O1 atom spontaneously and strongly binds with nearest-neighbor O on the lattice site to form an O2 molecule. The results also show that interstitial Tii2 affects little host lattice and the interstitial Oi would spontaneously bind to lattice oxygen. By investigating the calculated defect formation energies，we found that under the O-rich condition，the VTi1 and Oi formation are favorable，however，under the Ti-rich condition，although the point defects of Tii2 and VO1 easily appear，the formation energy of the Tii2 is lower than that of the VO1. Finally，to determine the relative stability of the point defects，the formation enthalpies of several point defects were considered.