First-principles have been calculated to investigate the phase stabilities of the intermetallic phase of MgAl2 compounds by electronic structures and the charge distribution maps.The first-principles employed the norm-conserving pseudo potential density functional method.They were calculated both with the Ceperley and Alder data as parameterized by Perdew and Zunger(CA-PZ) of local-density approximation (LDA) and with the Perdew Burke Eruzerh (PBE) form of gradient-corrected approximation (GGA).A better method was found by comparing results from these two ultrasoft pseudo potentials.The present calculations indicate that LDA is better than GGA compared with references.This work also compared the lattice parameters,cohesive energy,formation enthalpy and electronic structure between theoretical results and experimental measurements (where available).The calculations indicate that the unit cell volume get smaller after optimized and cohesive energy and formation enthalpy of C14 structure is the highest.The calculated structures are stable and the stability is aligned as C36 ＜ C15 ＜ C14.