Based on the variation principle, many methods have been developed in atomic structure calculations. A high quality complete basis set is essential to the calculation of atomic structures. We present how to construct quasi-complete basis sets through Dirac-Fock calculations and multi-configuration Dirac-Fock self-consistent filed calculations by using the full-relativistic GRASPVU program package, which is based on the multi-configuration Dirac-Fock method. The relativistic configuration interaction calculations are carried out by using the quasi-complete basis sets to adequately consider correlations. The relativistic retardation effect of electromagnetic interactions and the quantum electron dynamic corrections are also taken into account. Our calculation results of He agree well with other theoretical results and experimental results, which validates the feasibility of our calculation scenario. Our calculations are full-relativistic, and can be extended to high Z helium-like ions in which the relativistic effect is important. Our scenario of constructing quasi-complete basis sets can be used in any many-electron atomic system. We calculated the energy levels of Mg and elucidated the mechanism of its interesting fine-structure splittings of 3 3D and 4 3D levels.