A series of polymer semiconductors incorporating 2,1,3-benzothiadiazole-5,6-dicarboxylicimide (BTZI) as strong electron-withdrawing unit and an alkoxy-functionalized head-to-head linkage containing bithiophene or bithiazole as highly electron-rich co-unit are designed and synthesized. Because of the strong intramolecular charge transfer characteristics, all three polymers BTZI-TRTOR (P1), BTZI-BTOR (P2), and BTZI-BTzOR (P3) exhibit narrow bandgaps of 1.13, 1.05, and 0.92 eV, respectively, resulting in a very broad absorption ranging from 350 to 1400 nm. The highly electron-deficient 2,1,3-benzothiadiazole-5,6-dicarboxylicimide and alkoxy-functionalized bithiophene (or thiazole) lead to polymers with low-lying lowest unoccupied molecular orbitals (-3.96 to -4.28 eV) and high-lying highest occupied molecular orbitals (-5.01 to -5.20 eV). Hence, P1 and P3 show substantial and balanced ambipolar transport with electron mobilities/hole mobilities of up to 0.86/0.51 and 0.95/0.50 cm(2) V-1 s(-1), respectively, and polymer P2 containing the strongest donor unit exhibited unipolar p-type performance with an average hole mobility of 0.40 cm(2) V-1 s(-1) in top-gate/bottom-contact thin-film transistors with gold as the source and drain electrodes. When incorporated into bulk heterojunction polymer solar cells, the narrow bandgap (1.13 eV) polymer P1 shows an encouraging power conversion efficiency of 4.15% with a relatively large open-circuit voltage of 0.69 V, which corresponds to a remarkably small energy loss of 0.44 eV. The power conversion efficiency of P1 is among the highest reported to date with such a small energy loss in polymer:fullerene solar cells.