The fluorine incorporation into HfO2 with oxygen vacancies has been investigated using first principles calculations. The authors show that atomic fluorine can efficiently passivate the neutral oxygen vacancy with excess energies of 4.98 and 4.39 eV for threefold- and fourfold-coordinated oxygen vacancy sites, respectively. The introduction of fluorine elevates the vacancy induced state into conduction band by transferring the neutral vacancy state to positively charged state, and thus removes the gap state which causes trap-assisted tunneling. The HfO2 band gap is not narrowed after fluorine incorporation.