The medium band gap donor-acceptor (D-A) copolymer J61 based on bi(alkylthio-thienyl)benzodithiophene as donor unit and fluorobenzotriazole as acceptor unit and thiophene as π-bridge has demonstrated excellent photovoltaic performance as donor material in nonfullerene polymer solar cells (PSCs) with narrow bandgap n-type organic semiconductor ITIC as acceptor. For studying the effect of π-bridges on the photovoltaic performance of the D-A copolymers, here we synthesized a new D-A copolymer J61-F based on the same donor and acceptor units as J61 but with furan π-bridges instead of thiophene. J61-F possesses a deeper the highest occupied molecular orbital (HOMO) level at −5.45 eV in comparison with that (−5.32 eV) of J61. The non-fullerene PSCs based on J61-F:ITIC exhibited a maximum power conversion efficiency (PCE) of 8.24% with a higher open-circuit voltage (Voc) of 0.95 V, which is benefitted from the lower-lying HOMO energy level of J61-F donor material. The results indicate that main chain engineering by changing π-bridges is another effective way to tune the electronic energy levels of the conjugated D-A copolymers for the application as donor materials in non-fullerene PSCs.