Six novel conjugated copolymers (P1-P6) containing coplanar cyclopentadithiophene (CPDT) units (incorporated with bithiazole/thienyl-based monomers) were synthesized and developed for the applications of polymer solar cells (PSCs). Copolymers P1-P6 covered broad absorption ranges from UV to near-infrared (400-800 nm) with narrow optical band gaps of 1.70-1.94 eV, which are compatible with the maximum solar photon reflux. Partially reversible p- and n-doping processes of P1-P6 in electrochemical experiments were observed. Compared with those previously reported CPDT-based narrow band gap polymers, the proper molecular design for HOMO/LUMO levels of P1-P6 induced relatively high photovoltaic open-circuit voltages in the PSC devices. Powder X-ray diffraction (XRD) analyses suggested that these copolymers formed highly self-assembled π-π stackings. Under 100 mW/cm2 of AM 1.5 white-light illumination, bulk heterojunction PSC devices containing an active layer of electron donor copolymers P1-P6 blended with electron acceptor [6,6]-phenyl C61 butyric acid methyl ester (PCBM) in the weight ratio of 1:1 were explored, and the external quantum efficiency (EQE) measurements showed a maximal quantum efficiency of 60%. The PSC device containing P4 in the weight ratio of 1:2 with PCBM gave the best preliminary result with an overall power conversion efficiency (PCE) of 3.04%, an open-circuit voltage of 0.70 V, a short-circuit current of 8.00 mA/cm2, and a fill factor of 53.7%.