With the concept of super-atom, first principles calculations propose a new type of super stable cage clusters AlnH3n that are much more energetic stable than the well established clusters, AlnHn+2. In the new clusters, the aluminum core-frame acts as a super-atom with n vertexes and 2n Al-Al edges, which allow to adsorb n hydrogen atoms at the top-site and 2n at the bridge-site. Using Al12H36 as the basic unit, stable chain structures, (Al12H36)m, have been constructed following the same connection mechanism as for (AlH3)n linear polymeric structures. Apart from high hydrogen percentage per molecule, calculations have shown that these new clusters possess large heat of formation values and their combustion heat is about 4.8 times of the methane, making them a promising high energy density material.