Poly(3-hexylthiophene) (P3HT) is a low-cost polymer donor for organic solar cells (OSCs). However, the P3HT-based OSCs usually give low power conversion efficiencies (PCEs) due to the wide bandgap and the high-lying energy levels of P3HT. To solve this problem, in this work, we design and synthesize a new AD-A type non-fullerene acceptor, DFPCBR, which owns an electron-donating (D) core constructed by linking a 2,5-difluorobenzene ring with two cyclopentadithiophene moieties, and two electronaccepting (A) end-groups of benzo[c] [1,2,5]thiadiazole connected with 3-ethyl-2-thioxothiazolidin-4-one. Because of the strong electron-donating ability and large conjugation effect of D core, DFPCBR shows appropriate energy levels and a narrow bandgap matching well with those of P3HT. Therefore, with P3HT as the donor and DFPCBR as the acceptor, the OSCs possess broad absorption range from 350 nm to 780 nm and the reduced energy loss (Eloss) of 0.79 eV (compared with~1.40 eV for the P3HT:PC61BM device), providing a good PCE of 5.34% with a high open-circuit voltage (VOC) of 0.80 V. Besides, we observe that the photovoltaic performances of these devices are insensitive to the thickness of the active layers:even if the active layer is as thick as 320 nm,~80% of the best PCE is maintained, which is rarely reported for fullerene-free P3HT-based OSCs, suggesting that DFPCBR has the potential application in commercial OSCs in the future.