Phosphoric acid crystal doped with bivalent cation is easy to form pyrophosphate structure (P₂O₇) ^4-. This kind of oxide material containing pyrophosphate structure is very suitable for proton conductor, fuel cell, gas sensor, and ceramic film, etc. In this research we applied first principles to study the structural behaviour of oxygen vacancy in LuPO₄ crystal. The results showed that oxygen vacancies with two positive charges distort structure largely and form pyrophosphate structure. In order to verify the feasibility of this structure transition, the nudged elastic band method is used to find the highest saddle point of potential energy. The calculated results show that transition state energies of oxygen vacancy with +1 and +2 charge forming pyrophosphate structure are about 2.4 and 0 eV, respectively. So pyrophosphate structure easily forms for oxygen vacancy with +2 charge. Finally, the lattice structure, density of states and charge density distribution are obtained. P atom and O atom around the oxygen vacancy with +2 charge can form chemical bond. The electron on the P s will shift to O p orbit for oxygen with strong electronegative, which introduces the defect level in forbidden band. It is indicated that the property of the crystal changes drastically for the existence of the oxygen vacancy with two positive charges.