Fully conjugated donor acceptor block copolymers composed of poly(3-hexylthiophene) and poly(naphthalene bisimide) segments, P3HT-PNBI-P3HTs, were synthesized using quasi-living Grignard metathesis polymerization and the Yamamoto coupling reaction. Broad absorption in a range of 350-850 nm, which corresponded to the optical band gap of 1.46 eV, was observed for the P3HT-PNBI-P3HT thin films. In addition, the optical band gap decreased to 1.38 eV (the light absorption band extended to 893 nm) by thermal annealing, which was much smaller than those of previously reported donor-acceptor block copolymers (1.6-1.8 eV). The annealed P3HT:P3HT-PNBI-P3HT blend film (1:1 by weight) also exhibited broad absorption in the range of 350-950 nm. Cyclic voltammetry demonstrated that the P3HT-PNBI-P3HT thin films exhibited the oxidation and reduction properties derived from the P3HT and PNBI segments. The HOMO and LUMO levels were in the range of 5.57-5.60 and 4.22-4.27 eV, respectively. All-polymer solar cells using the P3HT:P3HT-PNBI-P3HT blend films achieved a power conversion efficiency of 1.28% with open-circuit voltage of 0.56 V, short-current of 4.57 mA/cm(2), and fill factor of 0.50.