Six conjugated donor-acceptor copolymers were designed by choosing benzo[1,2-c:4,5-c'] bis[1,2,5]-thiadiazole or [1,2,5] thiadiazolo [3,4-g] quinoxaline as the acceptor and thiophene, thieno [3,2-b] thiophene or dithieno [2,3-b:2',3'-d] thiophene as the donor unit. The electronic structure and properties of the designed copolymers were investigated systematically using the hybrid density functional theory method. The properties of the donor and acceptor moieties, especially the properties of the electron-donating and the electron-accepting ability, play a very important role in the geometric and electronic structures for the D-A copolymers. The theoretical study shows that the bridge bond length decreases regularly with an increase in the electron-accepting ability of electron acceptor, and increases regularly with an increase in the electron-donating ability of electron donor. In addition, the intramolecular charge transfer between the donor and acceptor moieties increases with an increase in the electron-accepting ability of acceptor and the electron-donating ability of donor. It is found that the band gap of the D-A copolymers is mainly controlled by the bond-length alternation along the main chain. The energy gap decreases with decreasing bond-length alternation. Namely, the band gap is decreased systematically with the decrease of bond-length alternation in the main chain. Among the designed copolymers, polymer p-BBT-TT is a very good candidate for an electrically conductive material due to its very small band gap (0.48 eV), large bandwidth and small effective mass of holes and electrons.