The atomic-level tunability that results from alloying multiple transition metals with d electrons in concentrated solid solution alloys (CSAs), including high-entropy alloys (HEAs), has produced remarkable properties for advanced energy applications, in particular, damage resistance in high-radiation environments. The key to understanding CSAs radiation performance is quantitatively characterizing their complex local physical and chemical environments. In this study, the local structure of a FeCoNiCrPd HEA is quantitatively analyzed with X-ray total scattering and extended X-ray absorption fine structure methods. Compared to FeCoNiCr and FeCoNiCrMn, FeCoNiCrPd with a quasi-random alloy structure has a strong local lattice distortion, which effectively pins radiation-induced defects. Distinct from a relaxation behavior in FeCoNiCr and FeCoNiCrMn, ion irradiation further enhanced the local lattice distortion in FeCoNiCrPd due to a preference for forming Pd-Pd atomic pairs.