In the current article, we investigated adsorption properties of Nickel (Ni), Copper (Cu), Cadmium (Cd) and silver (Ag) heavy metal atoms with zinc oxide (ZnO) nanotube and ZnO-graphene like structures sheet using Abinitio based density functional theory (DFT) calculations. At first, both nanostructures were optimized and then most stable configuration, adsorption energy and equilibrium distance of each heavy metal with nanostructures were computed via DFT and the results were compared with each other. Our obtained results reveal that Zn0nanotube had a better adsorbing behavior comparing to ZnO-graphene sheet case by case due to lower equilibrium distance and higher adsorption energy. This nanostructure created a strong binding with Ni, Cu and Ag but adsorption energy for Cd was clearly lower than others. Also, only Ni and Cu could have a chemisorption adsorption with the ZnO-graphene sheet and others showed a nearly weak physisorption adsorption with this nanostructure. The maximum adsorption energy for both ZnO-nanostructures occurred for nickel which were about -3.45 eV and -2.19 eV respectively. The minimum adsorption energy for ZnO nanotube occurred with Cd (-1.3 eV) while for ZnO-graphene sheet it occurred with Zn (-0.15 eV). In almost all items equilibrium distance decreased with increasing in adsorption energy. Moreover, we generated density of state (DOS) diagrams to investigate the electrical properties of studied structures.