Potential energy curves and dipole moments of five bound states are computed by high-level multi-reference configuration interaction method with all-electron aug-cc-pwCV5Z+DK for Mg atom and aug-cc-pV5Z-PP for I atom. To obtain high precise spectroscopic properties, Davidson modification, core valence correlation and relativistic correction are introduced. Based on PECs of 5 bound states, accurate spectroscopic constants, vibration levels and molecular constants of bound states are obtained by solving radial Schrödinger equation. Compared with recent theoretical calculation our results are closer to experimental datum. It shows that high precision calculation method and correlation correction are necessary for analysis of spectral properties. It provides support for further research on spectroscopic and transition characters of higher excited states of MgI molecule.