Based on a new n-type building block 5,5′-bibenzo[c][1,2,5]thiadiazole (BBT), we designed and synthesized a carbazole–BBT D–A copolymer (P1), and compared it with its carbazole–benzo[c][1,2,5]thiadiazole (BT) analog P2. P1 has good solubility in common organic solvents, while P2 has poor solubility. In films, P1 and P2 exhibit absorption maxima at 565 and 614 nm, respectively. The HOMO level of P1 is −5.51 eV, 0.18 eV lower than that of P2, while the LUMO level of P1 is −3.56 eV, slightly lower than that of P2. The low-lying energy levels and blue-shifted absorption of P1 are attributed to the stronger electron-withdrawing ability of BBT and the twisted main chain of P1. The field-effect hole mobility of P1 is 2 × 10−3 cm2 V−1 s−1. Polymer solar cells based on P1:PC71BM (1:3, w/w) exhibit a power conversion efficiency up to 3.7% with a high open circuit voltage of 0.98 V under an AM 1.5 simulated solar light at 100 mW cm−2.