Organolead halide perovskite solar cells have achieved a certified power-conversion efficiency (PCE) of 22.1% and are thus among the most promising candidates for next-generation photovoltaic devices. To date, most high-efficiency perovskite solar cells have employed arylamine-based hole-transport materials (HTMs), which are expensive and have a low mobility. The complicated doping procedures and the potentially stability-adverse dopants used in these HTMs are among the major bottlenecks for the commercialization of perovskite solar cells (PSCs). Herein, we present a polythiophene-based copolymer (PDVT-10) with a hole mobility up to 8.2 cm²·V^-1·s^-1 and a highest occupied molecular orbital level of -5.28 eV as a hole-transport layer (HTL) for a PSC. A device based on this new HTM exhibited a high PCE of 13.4% under 100 mW·cm^-2 illumination, which is one of the highest PCEs reported for the dopant-free polymer-based HTLs. Moreover, PDVT-10 exhibited good solution processability, decent air stability, and thermal stability, making it a promising candidate as an HTM for PSCs.