On the basis of tight-binding model, the electronic structure of graphene doped with N atoms is investigated. A set of wave functions of $2s$- and $2p$-states of noninteracting neutral C atoms are chosen as the basis. In a given study, the first three coordination spheres are taken into account for calculation of Hamiltonian matrix elements. As found, the hybridization of bands leads to a splitting of the energy spectrum of electrons in the Fermi energy region. Due to the overlapping of the energy bands, the above-mentioned gap manifests itself as quasi-gap, in which the electron density of states has a much lower value in comparison with other areas of the spectrum.