Simulation calculations for the oxygen-atom vacancy in the high temperature superconductor TlBa₂Ca_n-1Cu_nO_2n+2.5 (n=1) have been performed by means of the tight-binding approximation based on the EHMO method. The results indicate that the effect of the oxygen-atom vacancy on the charge distributions at the Tl-, Ba-, Cu- and O-atom sites is appreciably different and that there may exist two kinds of Cu cation with different net charges ( approximately +3.0 or approximately +1.0) due to the oxygen-atom vacancy in the lattice. The electric field gradient at the site of the oxygen-atom vacancy has been calculated. The position of the oxygen-atom vacancy which favours the high temperature superconductivity of TlBa₂Ca_n-1Cu_nO_2n+2.5 (n=1) has been discussed.