Quantum-chemical semi-empirical molecular-orbital calculations of zigzag graphene nanoribbons (nzGNRs) were done for the number of zigzag carbon chains and 10. The antiferromagnetic (AFM) nature of zGNRs’ ground state was confirmed. The energy difference between AFM and ferromagnetic (FM) states was calculated, and dimerization patterns of their chemical bond lengths were elucidated. The electron energy band structure calculations show that narrow nanoribbon (4 zGNR) is semiconducting in both AFM and FM states. For wider nanoribbon (10 zGNR), the AFM state is semiconducting ( band gap), whereas the FM state is half-metallic (electrical conduction with only one spin orientation).