The geometries, stabilities, and electronic properties of B-n and AlBn clusters, up to n = 12, have been systematically investigated by using the density-functional approach. The results of B-n clusters are in good agreement with previous conclusions. When the Al atom is doped in B-n clusters, the lowest-energy structures of the AlBn clusters favor two-dimensional and can be obtained by adding one Al atom on the peripheral site of the stable B-n when n <= 5. Starting from n = 6, the lowest-energy structures of AlBn clusters favor three-dimensional and can be described as an Al atom being capped on the B-n clusters. The average atomic binding energies, fragmentation energies, and second-order energy differences are calculated and discussed. Maximum peaks were observed for clusters of sizes n = 5, 8, 11, especially for the AlB8 cluster, implying that these clusters possess relatively higher stability. The adiabatic IP and EA of AlBn and B-n clusters are discussed and compared with some available experimental results. A distinct phenomena for AlBn clusters is that all even n, but n = 10, have higher adiabatic ionization potentials than odd n.