In this work, a medium-bandgap polymer POBDFBT was synthesized and served as the single donor in binary and ternary polymer solar cells (PSCs) together with two acceptors (MC and PC71BM). A promising power conversion efficiency (PCE) of 7.91% with a high short-circuit current density (J(SC)) of 17.65 mA cm(-2) is achieved from the ternary PSC without any cathode modification layer. The enhancement of J(SC) in ternary PSCs can be attributed to the complementary absorption and cascade-like energy level of the two acceptors. With alkoxyl substitution in the electron-donating unit, POBDFBT presents good miscibility with ITIC and PC71BM respectively, while a more optimized morphology of the ternary bulk heterojunction (BHJ) lead to the enhanced and balanced hole/electron mobility of the devices. Our results demonstrate a facile method for developing new polymeric donors for serving as the universal donors in binary and ternary PSCs.