A new conjugated D-A copolymer, TBFBT, containing a fluorinated benzothiazole electron-acceptor unit and an electron-donor segment of alkylthienyl substituted thieno[2,3-f]benzofuran, was synthesized using a Stille coupling reaction. The resulting copolymer was characterized by elemental analysis, GPC, TGA, UV-Vis absorption spectroscopy and cyclic voltammetry measurements. The copolymer was readily dissolved in common organic solvents, exhibited good film forming properties and displayed a broad absorption from 300 nm to 800 nm with a low optical bandgap of 1.56 eV. Cyclic voltammetry measurement gave HOMO and LUMO energy levels of -5.11 eV and -3.49 eV, respectively. Polymer solar cells based on TBFBT: PC61BM (1:1.5, w/w) demonstrated an initial power conversion efficiency (PCE) of 4.1% with a Voc of 0.72 V and a Jsc of 11.6 mA cm-2. PSCs based on TBFBT:PC71BM (1:1.5, w/w, 3 vol% 1,8-diiodooctane as additive) were further optimized by using methanol. The optimized result exhibited a high PCE up to 6.1% with a high Jsc of 14.4 mA cm-2 and FF of 0.62, under the illumination of AM1.5G, 100 mWcm-2. These investigations indicate that the new copolymer TBFBT is a promising donor material for PSCs and methanol treatment is a simple and effective way to improve PCE.