Metallic phases of Al2H and AlH at megabar pressures are predicted to be possible by using ab initio density functional calculations. The Al2H phase is stabilized above 155 GPa, where several candidate structures are quite competitive; the structural properties suggest that Al2H has the phase where Al atoms form an hcp structure and H atoms occupy the octahedral sites in a random manner. The AlH phase is stable above 175 GPa, where the structure takes R3m symmetry. Superconducting transition temperature (Tc) of the Al2H phase is estimated to be of the order of 1 K. In contrast, Tc of the R3m AlH reaches 58 K at 180 GPa. The electronic structures around the Fermi energy in the R3m AlH are insensitive to pressure compared with those in the well-known Pm3n phase of AlH3. Accordingly, while theoretical Tc of the Pm3nAlH3 rapidly decreases with compression and becomes almost zero above ∼200 GPa, that of the R3m AlH remains to be 21 K even at 335 GPa. This means that although superconductivity was not observed experimentally in AlH3, it might be achieved in AlH.