The structural and electronic properties of Si(335)-Au surface decorated with Pb atoms are studied by means of density-functional theory. The resulting structural model features Pb atoms bonded to neighboring Si and Au surface atoms, forming monoatomic chain located 0.2 nm above the surface. The presence of Pb chain leads to a strong rebonding of Si atoms at the step edge. The fact that Pb atoms occupy positions in the middle of terrace is consistent with STM data, and also confirmed by simulated STM images. The calculated band structure clearly shows one-dimensional metallic character. The calculated electronic bands remain in very good agreement with photoemission data.