The electronic structure and properties of polypyrrole (p-Pyr) based substituting by the group of pyrazine (Pyz) and their model compounds were studied by the density functional theory (DFT) at the B3LYP level with 6-31G* basis set. The bond length, the topological analyses and nucleus-independent chemical shifts (NICS) were analyzed and correlated with the electronic properties. The bond length of all compounds is reduced with the increase in the degree of polymerization, and the band gap of these compounds is decreased. The change of NICS shows that the conjugation degree in central section of the polymeric axis is stronger than that in outer section, and the structure of central part was close to quinoid structure in polymers. The theoretical results suggest that the band gap of p-Pyz (polymer of Pyz) (0.37 eV) is much smaller than the band gap of polypyrrole (1.84 eV). The narrow band gap, large HOMO and LUMO bandwidths and small effective masses make p-Pyz have a remarkable elevation of the conductivity, so it may be considered as a very good candidate for conducting material.