Metal-Organic Networks (MON’s) is the central bone for the chemical compounds of the latest study for the energy department. The study of MON’s structure provides us numerous benefits in different fields related to chemical sciences, electrical and civil sectors. The MON’s structure is also used to restore different chemical compounds, especially those elements which can be used for the energy purpose such as hydrogen and carbon. Topological indices of the MON’s structure provide relationships between physical and chemical characteristics of the this compound such as melting points, boiling points, chemically stability, pressure, chemical reaction factors and many other basic properties. In this paper we calculate different topological indices based on first, second and third distances for two different metal-organic networks with expanding number of layers consisting on both organic ligands and metal vertices. A comparison between the calculated different kinds of the Topological Indices with the help of the numerical values and their graphical representation is also included.