In the one-band tight-binding model, the influence of substitutional impurities on the energy spectrum and electrical conductivity of graphene is studied. As determined, the ordering of substitutional impurity atoms on nodes of the crystal lattice causes the appearance of a gap in the energy spectrum of graphene with width $\eta|\delta|$ centred at the point $y\delta$, where $\eta$ is the parameter of ordering, $\delta$ is the difference of the scattering potentials of impurity and carbon atoms, and $y$ is the impurity concentration. If the Fermi level falls in the region of the mentioned gap, then the electrical conductivity $\sigma_{\alpha\alpha} → \infty$ at the ordering of graphene, $i.e.$, the metal–dielectric transition arises. If the Fermi level is located outside the gap, then the electrical conductivity increases with the parameter of order $\eta$ by the relation $\sigma_{\alpha\alpha} \approx (y^2 - (1/4)\eta^2)^{-1}$. At the concentration $y$ = 1/2, when the ordering of impurities $\eta$ → 1, the electrical conductivity of graphene $\sigma_{\alpha\alpha} → \infty$, $i.e.$, the transition of graphene in the state of ideal electrical conductance arises. The localization region of impurity electronic states, which arise at the edges of the spectrum and edges of the energy gap, is investigated.