Small-molecule donor/polymer acceptor bulk-heterojunction films with both compounds strongly absorbing have great potential for further enhancements of performance of organic solar cells. By employing a newly synthesized small molecule donor with a commercially available polymer acceptor in a solution-processed fullerene-free system, we report a high power conversion efficiency of close to 4%. Detailed investigation reveals that the record FF value of the small-molecule donor/polymer acceptor system of over 60% is related to the good charge carrier transport properties and low recombination losses; while efficient exciton dissociation/charge transfer comes along with a remarkably low energetic driving force of ~0.06 eV, which ensures the most optimized open-circuit voltage of all organic solar cells studied to date. Despite the more limited exciton dissociation compared to that in a small molecule/fullerene solar cell, the stronger absorption of the N2200 acceptor, allows for a rather comparable photocurrent to be extracted, and thus an overall superior photovoltaic performance.