Three kinds of donor-acceptor (D-A) type photovoltaic polymers were synthesized based on 2,7-carbazole and thieno[3,4-c] pyrrole-4,6-dione (TPD). The conjugation of weakly electron (e)-donating 2,7-carbazole and strongly e-accepting TPD moieties yielded a deep highest occupied molecular orbital (HOMO) and its energy level was fine-controlled to be -5.72, -5.67 and -5.57 eV through the incorporation of thiophene (T), thieno[3,2-b]thiophene (TT) and bithiophene (BT) as a pi-bridge. Polymer:[6,6]-phenyl-C-71 butyric acid methyl ester (PC71BM) based bulk heterojunction solar cells exhibited a high open-circuit voltage (V-OC) in the range, 0.86-0.94 V, suggesting good agreement with the measured HOMO levels. Despite the high V-OC, the thiophene (or thienothiophene)-containing PCTTPD (or PCTTTPD) showed poor power conversion efficiency (PCE, 1.14 and 1.25%) because of the very low short-circuit current density (J(SC)). The voltage-dependent photocurrent and photoluminescence quenching measurements suggested that hole transfer from PC71BM to polymer depends strongly on the HOMO level of the polymer. The PCTTPD and PCTTTPD devices suffered from electrone-hole recombination at the polymer/PC71BM interfaces because of the insufficient energy offset between the HOMOs of the polymer and PC71BM. The PCBTTPD:PC71BM device showed the best PCE of 3.42% with a V-OC and J(SC) of 0.86 V and 7.79 mA cm(-2,) respectively. These results show that photovoltaic polymers should be designed carefully to have a deep HOMO level for a high V-OC and sufficient energy offset for ensuring efficient hole transfer from PC71BM to the polymer. (C) 2015 Elsevier B.V. All rights reserved.