The Hartree-Fock-Bogolyubov (HFB) theory is a good theoretical approximation for describing the nuclear structure of neutron-rich deformed nuclei, it is generalized the HF theory with BCS pairing theory. In this work, ground-state properties of even-even 76Os, 78Pt, 80Hg and 82Pb isotopes from proton drip-line to neutron drip-line have been studied in the framework of the axially deformed Hartree-Fock-Bogoliubov (HFB) method with two Skyrme nucleon-nucleon force HFB9 and UNE1. The numerically calculated results of binding energy, two neutron separation energy, two neutron shell gap, quadrupole deformation, neutron pairing gap and charge radius are discussed and compared with the available values of the experiment, Finite Range Droplet Model (FRDM), Relativistic Mean-Field (RMF) and Hartree-Fock-Bogoliubov based on D1S Gognay force. The energy surface curves are plotted for some isotones of the investigated nuclei, the transition in the shapes was clear with the change in the number of neutrinos. Our calculations show good agreements in comparison with other data and results.