The present work aims at experimentally clarifying the structure change of neutron-rich Mg isotopes as a function of the neutron number by firmly establishing the level schemes of the Mg isotopes in a wide excitation energy range. We use our unique method of beta-decay spectroscopy which takes advantage of anisotropic beta decay of spin-polarized Na isotopes. The asymmetry parameters of the beta-decay are the effective tool to unambiguously assign the spin-parity of levels in the daughter nucleus. As the first step of the systematic studies on neutron-rich Mg isotopes from lighter region outside of the N = 20 "island of inversion" to heavier one across through the island, very detailed level scheme of Mg-28 and Mg-29 have been successfully established at TRIUMF, where the world-highest polarized alkali beams are available.