A new hole-transport layer, poly(3,4-ethylenedioxythiophene):poly(styrene sulfonate (PEDOT:PSS) with intercalated polyethylene glycol (PEG), was introduced into Pb-free inverted Formamidinium Tin Triiodide (FASnI3) perovskite solar cells to reduce the energy-level mismatch between FASnI3 and PEDOT:PSS. Intercalation of PEG into the PEDOT:PSS enhanced the power conversion efficiency from 2.01% to 5.12% in the forward scan and resulted in high reproducibility. The device based on PEG-PEDOT:PSS showed a reduced hysteresis and a stabilized efficiency of 4.91%. Finally, the devices with the new hole-transport layer retained more than 90% and 95% of their initial power conversion efficiencies upon storage in, respectively, an ambient environment for 4 h and a N2 environment for 30 days. These findings suggest that this new material will facilitate the development of environment-friendly Pb-free perovskite solar cells for real-world applications.