The structural and electronic properties of gold decorated Si(335) surface are studied by means of density-functional calculations. The resulting structural model indicates that the Au atoms substitute some of the Si atoms in the middle of the terrace in the surface layer. Calculated electronic band structure near the Fermi energy features two metallic bands, one coming from the step edge Si atoms and the other one having its origin in hybridization between the Au and neighboring Si atoms in the middle of the terrace. The obtained electronic bands remain in good agreement with photoemission data.