Geometric configurations and harmonic frequencies of AlHn(n=1—3) molecule, their univalent cation and univalent anion have been calculated by means of b3lyp and qcisd methods at 6-311++g** level with Gaussian03 software packages. Dissociation energies, first vertical ionization energies, electron affinities of the neutral molecules are studied. We compared the above theoretical values with experimental values and other theoretical values from literatures, and found that the values from qcisd method are closer to experimental values, the bond length of AlHn(n=1—3) and their univalent cation shorten with the H atom numbers increasing in AlHn molecule. That is to say, the Al atom attracts H atoms stronger as the number of the H atoms increases and electronic cloud are closer to aluminum atom. The computational results show that the equilibrium pressure of AlH3 is higher than that of NiH, but it is rather low still. For the AlH3 molecule we have the results: De=9.3705eV,ΔG0=-163.373kJ at 298.15K, so the AlH3 molecule is more stable thermodynamically. The problem is that AlH3 molecule is easier to dissociate and produce hydrogen gas. It may be stable if preserved in hydrogen gas environment.