Polymer hole-transport layer (HTL) materials have gained considerable attention because of their solution processability, which is effective for maintaining mechanical flexibility for printing technology in perovskite solar cells (PSCs). However, these materials have low carrier mobility that is insufficient to transport charge carriers. The doping process is usually employed to overcome this drawback, but it adversely affects the device stability. In this study, a dopant-free P18, which is composed of rigid and coplanar thienylenevinylene and dithienothiophene, is used as a HTL in PSCs. These units consist of thiophene which can coordinate with Pb2+ atoms as Lewis bases in order to suppress charge recombination on the perovskite surface and grain boundary. The PSCs fabricated with the dopant-free P18 present a power conversion efficiency of 14.8%, which is higher than that with doped P3HT (13.9%). Furthermore, the PSC fabricated with the dopant-free P18 can maintain a performance of 60% under the humidity conditions of 70–80% after 200 hours without encapsulation by limiting the hygroscopic dopant in the HTL, which is superior to those fabricated with doped P3HT (25%). The results of this study demonstrate that the high-mobility thiophene-based conjugated polymers can act as highly efficient and stable dopant-free HTL materials in PSCs.