Stabilizing high-efficiency perovskite solar cells (PSCs) at operating conditions remains an unresolved issue hampering its large-scale commercial deployment. Here, we report a star-shaped polymer to improve charge transport and inhibit ion migration at the perovskite interface. The incorporation of multiple chemical anchor sites in the star-shaped polymer branches strongly controls the crystallization of perovskite film with lower trap density and higher carrier mobility and thus inhibits the nonradiative recombination and reduces the charge-transport loss. Consequently, the modified inverted PSCs show an optimal power conversion efficiency of 22.1% and a very high fill factor (FF) of 0.862, corresponding to 95.4% of the Shockley-Queisser limited FF (0.904) of PSCs with a 1.59-eV bandgap. The modified devices exhibit excellent long-term operational and thermal stability at the maximum power point for 1000 hours at 45°C under continuous one-sun illumination without any significant loss of efficiency.