Scanning tunneling microscopy observations reveal that dosed Fe atoms are adsorbed at steps to form monatomic Fe wires on vicinal Au(111) surfaces. We found that decoration of step edges with Fe adatoms has a significant influence on the behavior of the surface state confined between regularly arranged steps. On a stepped surface with Fe monatomic rows, angle-resolved photoemission spectra measured in the direction perpendicular to the steps show parabolic dispersion, in contrast to one-dimensional quantum-well levels observed on a clean surface. Simple analysis using a one-dimensional Kronig-Penney model reveals potential barrier reduction from 20 eVÅ to 4.6 eVÅ, suggesting an attractive nature of the Fe adatoms as scatterers.