A new low band gap polymer P1 with fluorinated acenaphtho[1,2-b] quinoxaline (AQ) as the acceptor unit and benzo[1,2-b:4,5-b'] dithiophene as the donor unit has been designed and synthesized. Comparing with its non-fluorinated analog polymer P2, P1 shows a lower band gap of 1.76 eV with a deeper HOMO energy level of -5.54 eV. Polymer solar cells with the blend of P1 and PC71BM as the active layer without the additive or annealing showed a PCE of 4.72%, which was higher than P2 based devices with a PCE of 1.65%. Obviously, P1 can endow devices with a V-oc of 0.77 V and a J(sc) of 10.75 mA cm(-2), which are higher than that of P2 based devices with a V-oc of 0.75 V and a J(sc) of 4.41 mA cm(-2), such an enhanced photovoltaic performance can be attributed to the broader absorption, the improvement of film morphology, and the higher charge mobility. Thus, fluorinated AQ can be a useful acceptor unit to construct narrow band gap conjugated polymers. To the best of our knowledge, this is the highest PCE report for AQ based polymer solar cells. (C) 2015 Elsevier Ltd. All rights reserved.