The electronic state and chemical bonding of $eta$-MnO$_2$ with transition metal dopants were theoretically investigated by DV-X$_{alpha}$ (the discrete variational X$_{alpha}$) method, which is a sort of the first principles molecular orbital method using the Hartree-Fock-Slater approximation. The calculations were performed with a $_Mn_{14}$ MO$_{56}$ )$^{-52}$ (M = transition metals) cluster model. The electron energy level, the density of states (DOS), the overlap population, the charge density distribution, and the net charges, were calculated. The energy level diagram of MnO$_2$ shows the different band structure and electron occupancy between the up spin states and down spin states. The dopant levels decrease between the conduction band and the valence band with the increase of the atomic number of dopants. The covalency of chemical bonding was shown to increase and ionicity decreased in increasing the atomic number of dopants. Calculated results were discussed on the basis of the interaction between transition metal 3d and oxygen 2p orbital. In conclusion it is expected that when the transition metals are added to MnO$_2$ the band gap decreases and the electronic conductivity increases with the increase of the atomic number of dopants. the atomic number of dopants.