Graph theory has been studied different areas such as information, mathematics and chemistry sciences. Especially, it has been the most important mathematical tools for the study the analysis of chemistry. A topological index has been a numerical descriptor of the molecular structure derived from the corresponding molecular graph, also it has used vulnerability of chemical graphs. The vulnerability of a graph has been the reliability of the graph after the disruption of  some vertices or edges until breakdown. There are a lot of topological indices which have been defined. Furthermore, the diamond graphs have been defined recently. In this paper, exact formulas for the eccentricity-based topological indices of diamond graphs have been obtained.