Narrow-bandgap polymer semiconductors are essential for advancing the development of organic solar cells. Here, a new narrow-bandgap polymer acceptor L14, featuring an acceptor-acceptor (A-A) type backbone, is synthesized by copolymerizing a dibrominated fused-ring electron acceptor (FREA) with distannylated bithiophene imide. Combining the advantages of both the FREA and the A-A polymer, L14 not only shows a narrow bandgap and high absorption coefficient, but also low-lying frontier molecular orbital (FMO) levels. Such FMO levels yield improved electron transfer character, but unexpectedly, without sacrificing open-circuit voltage (V-oc), which is attributed to a small nonradiative recombination loss (E-loss,E-nr) of 0.22 eV. Benefiting from the improved photocurrent along with the high fill factor andV(oc), an excellent efficiency of 14.3% is achieved, which is among the highest values for all-polymer solar cells (all-PSCs). The results demonstrate the superiority of narrow-bandgap A-A type polymers for improving all-PSC performance and pave a way toward developing high-performance polymer acceptors for all-PSCs.