The most widely studied polymer-based solar cells consist of a bulk-heterojunction (BHJ) structure in which a conjugated polymer is mixed with a low-molecular-weight fullerene derivative. In these systems, the conjugated polymer acts as an electron donor (D) and the fullerene derivative acts as an acceptor (A). The power conversion efficiencies (PCEs) of polymer/fullerene BHJ solar cells have increased over the past two decades, and approached 10%. On the other hand, polymer/polymer blend (all-polymer) solar cells, composed of polymer donors and acceptors, have numerous advantages over the conventional fullerene-based organic solar cells, including flexible design and larger scope for tuning of optical, electronic, and morphological properties. In addition, the ease of solution processing, good thin-film formation property, morphological stability, and potentially low cost of polymer materials are great beneficial for future commercialization of all-polymer solar cells. Owing to these attractive features, all-polymer solar cells have gained significantly increasing attention in the field of chemistry for renewable energy. However, the PCE of all-polymer solar cells still mostly remains at 3-4%, lagging far behind the efficiency of polymer/fullerene BHJ solar cells. In this study, all-polymer BHJ solar cells consisting of low-bandgap polymer donor, poly[2,3-bis-(3-octyloxyphenyl)quinoxaline-5,8-diyl-alt-thiophene-2,5-diyl] (PTQ1) and polymer acceptor, poly{[N, N’-bis(2-octyldodecyl)-naphthalene-1,4,5,8-bis(dicarboximide)-2,6-diyl]-alt-5 ,5’-(2,2’-bithiophene)} (N2200) were fabricated. Because of the efficient light absorption at near-infrared wavelengths by both polymer D and A, the device consisting of a 50:50 blend of D:A resulted in a PCE as high as 3.4%. Moreover, the device performance increased further at the D:A blending ratio of 70:30 wt% to lead to a photocurrent density (JSC) of 8.85 mA cm2, fill factor (FF) of 0.55, open-circuit voltage (VOC) of 0.84 V, and the best PCE of 4.1%. In addition to the efficient light absorption at near-infrared wavelengths, the excitons generated in the D were effectively conveyed to the interface with the A via energy transfer. Moreover, the hole mobility in the blended film became more balanced with the electron mobility with an increase in the D content. Consequently, the overall device performance was optimized at the high D content. A high PCE exceeding 4% demonstrates the potential of all-polymer solar cells as an alternative to traditionally used fullerene-based solar cells.