Clear indication has it in numerous studies that a strong inherent relationship exists between the chemical characteristics of chemical compounds and drugs (e.g., boiling point and melting point) and their molecular structures. There are several topological indices are defined on these chemical molecular structures and they can help researchers better understand the physical features, chemical reactivity, and biological activity. The study of the topological indices on chemical structure of chemical materials and drugs, therefore, will make the chemical experiments complete. It will also provide a theoretical basis for the manufacturing of drugs and chemical materials. In this paper, by means of molecular structural analysis, we report several eccentric related indices of an infinite class of nanostar dendrimers.