The first and second Hyper-Zagreb indices are the molecular descriptors that describe the structures of chemical compounds and they help us to predict certain physicochemical properties. In this paper, we studied the first and second Hyper-Zagreb indices for certain important chemical structures like line graphs of the VC5C7[p, q] and HC5C7[p, q] nanotubes. Moreover, we defined second Hyper-Zagreb-polynomial of graph G and applied it on the line graphs of the VC5C7[p, q] and HC5C7[p, q] nanotubes. These explicit formulae can correlate the chemical structure of molecular graph of nanotube to information about their physical structure.