Converting solar energy into electricity provides a much-needed solution to the energy crisis the world is facing today. Polymer solar cells have shown potential to harness solar energy in a cost-effective way. Significant efforts are underway to improve their efficiency to the level of practical applications. Here, we report highly efficient polymer solar cells based on a bulk heterojunction of polymer poly(3-hexylthiophene) and methanofullerene. Controlling the active layer growth rate results in an increased hole mobility and balanced charge transport. Together with increased absorption in the active layer, this results in much-improved device performance, particularly in external quantum efficiency. The power-conversion efficiency of 4.4% achieved here is the highest published so far for polymer-based solar cells. The solution process involved ensures that the fabrication cost remains low and the processing is simple. The high efficiency achieved in this work brings these devices one step closer to commercialization.