Using first-principles pseudo-potential plane wave method, the energetics, geometrical and electronic structures of three Al13I cluster isomers were calculated. The calculation results of the binding energy indicate Al13I cluster is more stable than Al13 cluster although its electrons are not a magic number as in Al13 cluster, and among Al13I cluster isomers the "Bridge" structure is the most stable, the second is the "Ontop" structure, and the worst is the "Hollow" structure. By analyzing the geometrical structures of Al13I cluster isomers, it is found that after I atom and Al13 cluster combine the geometrical structures of Al13 moieties are changed besides Al13IHollow cluster, in which the Al13 moiety is still a regular icosahedron. For Al13IOntop cluster, the Al13 moiety has a shrinking trend to I, whereas in Al13IBridge cluster it is distorted. Mulliken population analysis shows for the interaction of electrons between Al(I atoms in Al13I cluster not only there exists an ionic bonding but there is a covalent bonding. Part of electrons in the Al13 cluster transfer to I as Al13 cluster and I atom combine. The order of the strength of covalent bonding between Al13 moiety and I in Al13I cluster isomers is Al13IBridge>Al13IHollow>Al13IOntop. Further analysis of electric structures of Al13 and Al13I clusters indicates a higher stability of Al13I cluster than Al13 cluster can be attributed to the s-p hybridization of 3s and 3p electrons of Al in Al13 moiety induced by I doped, which leads to fewer electrons N(EF) at EF in Al13I and a larger energy gap ΔEH-L between HOMO and LUMO levels in Al13I cluster. The distinguish of structural stability of Al13I cluster isomers mainly originates from their different magnitudes in decrease of N(EF) and increase of ΔEH-L relative to Al13 cluster. The fewest N(EF) and the largest ΔEH-L are responsible for the high stability of Al13IBridge cluster .