Density functional theory (DFT) calculations have been carried out to study the linear polymeric Al (n) H-3n (n = 1-12) clusters and cage Al (n) H-3n (n = 6, 8, 10, and 12) clusters. In particular, a stable cage-chain (Al12H36) (m) (m = 2, 3) structure has been predicted for the first time, with the basic unit, cage Al12H36 structure connected by double hydrogen-bridged bonds (i.e., Al-2H-Al). The stability of these clusters has been confirmed by the large binding energies and substantial energy gaps between the highest occupied molecular orbital and the lowest unoccupied molecular orbital, and the cage-chain structure is more stable than the corresponding chain and cage forms. Furthermore, with the cluster size increasing, the aluminum hydride clusters tend to exist with the cage structure compared with the chain structure, even though the formation of the chain structure is much easier than others. Also, the heats of formation for some clusters have been calculated by the atomization reaction method based on the results from DFT calculations, and it is revealed that the cage and cage-chain clusters can store more energy and, especially the latter, is more promising as a kind of energetic material.