The electronic structure and chemical bonding of β-MnO₂ were theoretically investigated by DV-X_α (the discrete variation X_α) method. which is a sort of the first principle molecular orbital method using Hatre-Fock-Slater approximation. The calculations on several cluster models having different sizes were carried out for the determination of a model suited for analyzing bulk state. The Mn₁₅O₅₆ model was selected as a sufficiently suitable model for the calculation of electronic state and chemical bonding by the comparison of the calculated XPS (X-ray photo-electron spectrum) and experimentally measured XPS. By using this model, the electron energy level, the density of state, the bond overlap population, the charge density distribution, and the net ionic transfer between cations and anions were calculated and discussed.