Although perovskite solar cells (PVSCs) have achieved rapid progress in the past few years, most of the high‐performance device results are based on the doped small molecule hole‐transporting material (HTM), spiro‐OMeTAD, which affects their long‐term stability. In addition, some defects from under‐coordinated Pb atoms on the surface of perovskite films can also result in nonradiative recombination to affect device performance. To alleviate these problems, a dopant‐free HTM based on a donor‐acceptor polymer, PBT1‐C, synthesized from the copolymerization between the benzodithiophene and 1,3‐bis(4‐(2‐ethylhexyl)thiophen‐2‐yl)‐5,7‐bis(2‐alkyl)benzo[1,2‐c:4,5‐c′]dithiophene‐4,8‐dione units is introduced. PBT1‐C not only possesses excellent hole mobility, but is also able to passivate the surface traps of the perovskite films. The derived PVSC shows a high power conversion efficiency of 19.06% with a very high fill factor of 81.22%, which is the highest reported for dopant‐free polymeric HTMs. The results from photoluminescence and trap density of states measurements validate that PBT1‐C can effectively passivate both surface and grain boundary traps of the perovskite.