We have investigated the formation of Mg vacancy induced by ultra-dilute trivalent impurities in MgO by a combination of positron annihilation measurement and theoretical calculations of positron lifetimes. The undoped MgO yields the shortest positron lifetime of 130 ps that is shorter than that of 166 ps previously reported using a single crystal sample. The positron lifetime of the doped samples increases with the increase of the Al or Ga dopant concentration and is saturated at around 170 ps. This result indicates that the previously reported value of 166 ps is ascribed to not the bulk but the vacancy state induced by impurities. The experimental bulk lifetime of 130 ps, which is obtained by employing trapping model, is well reproduced by the theoretical calculation using the semiconductor model. The calculated defect lifetime is about 20 ps longer than the experimental value. This may be due to the lattice relaxation around Mg vacancy associated with the trapping of positrons.