There are several important open questions that need to be addressed by exploring the nuclear landscape of the nuclei properties. The physics of rich neutron nuclei is one of the most subjects in nuclear structure physics both theoretically and experimentally. The Hartree-Fock-Bogolyubov (HFB) theory is a good theoretical framework for describing the nuclear structure of nuclei. Using HFB method with four different Skyrme types effective nucleon-nucleon interactions: SIII, SKM*, SLy4 and UNE0. The ground-state properties of even-even neutron-rich Mg isotopes have been investigated. Having different types of Skyrme-force parameterizations requires a continuous search for the best for describing the experimental data. Our results of protons and neutrons rms radii, neutrons skin thickness and neutrons density distributions have been compared with the available data of Hartree-Fock-Bogoliubov calculations based on the D1S Gogny interaction, and predictions of some nuclear theories such as Relativistic Mean Field (RMF) theory. Our investigated Skyrme functionals show good agreements in comparison with other data and results.