The static and dynamic polarizabilities for the lowest-energy structures of pure aluminum clusters up to 31 atoms have been investigated systematically within the framework of density functional theory. The size evolution of several electronic properties such as ionization potential, electron affinity, the energy gap between the highest occupied molecular orbital and lowest unoccupied molecular orbital, and chemical hardness have also been discussed for aluminum clusters. Our primary focus in this article, however, has been upon the study of polarizability of aluminum clusters, although we also looked at the role of other electronic properties. From the energetics point of view, the relative stability of aluminum clusters at different sizes is studied in terms of the calculated second-order difference in the total energy of cluster and fragmentation energy, exhibiting that the magic numbers of stabilities are n = 7, 13, and 20. Moreover, the minimum polarizability principle is used to characterize the stability of aluminum clusters. The results show that polarizabilities and electronic properties can reflect obviously the stability of clusters. Electronically, the size dependence of ionization potential and electron affinity of clusters is determined. On the basis of the Wood and Perdew model these quantities converge asymptotically to the value of the bulk aluminum work function.