Surface reconstructions and electronic structures of Au thin films formed on the Ag(111) surface have been investigated using low-temperature scanning tunneling microscopy. We find that striped patterns form even at a one-monolayer (ML) coverage of Au on the Ag(111) surface. In contrast to the striped patterns, hexagonal ring structures are observed on the 2 ML Au surface, where four rings are connected in a triangular arrangement as a single unit. The ring patterns disappear above 3 MLs, and the striped patterns reappear.