An effective way to improve polymer solar cell efficiency is to use a tandem structure, as a broader part of the spectrum of solar radiation is used and the thermalization loss of photon energy is minimized. In the past, the lack of high-performance low-bandgap polymers was the major limiting factor for achieving high-performance tandem solar cell. Here we report the development of a high-performance low bandgap polymer (bandgap <1.4 eV), poly[2,7-(5,5-bis-(3,7-dimethyloctyl)-5H-dithieno[3,2-b:2',3'-d]pyran)-alt-4,7-(5,6-difluoro-2,1,3-benzothia diazole)] with a bandgap of 1.38 eV, high mobility, deep highest occupied molecular orbital. As a result, a single-junction device shows high external quantum efficiency of >60% and spectral response that extends to 900 nm, with a power conversion efficiency of 7.9%. The polymer enables a solution processed tandem solar cell with certified 10.6% power conversion efficiency under standard reporting conditions (25 °C, 1,000 Wm(-2), IEC 60904-3 global), which is the first certified polymer solar cell efficiency over 10%.