Transition-metal chalcogenides (TMCs) materials have attracted increasing interest both for fundamental research and industrial applications. Among all these materials, two-dimensional (2D) compounds with honeycomb-like structure possess exotic electronic structures. Here, we report a systematic study of TMC monolayer AgTe fabricated by direct depositing Te on the surface of Ag(111) and annealing. Few intrinsic defects are observed and studied by scanning tunneling microscopy, indicating that there are two kinds of AgTe domains and they can form gliding twin-boundary. Then, the monolayer AgTe can serve as the template for the following growth of Te film. Meanwhile, some Te atoms are observed in the form of chains on the top of the bottom Te film. Our findings in this work might provide insightful guide for the epitaxial growth of 2D materials for study of novel physical properties and for future quantum devices.