The geometries, stabilities, and electronic properties of Bn and AlBn clusters, up to n=12, have been systematically investigated by using the density-functional approach. The results of Bn clusters are in good agreement with previous conclusions. When the Al atom is doped in Bn 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 Bn when n<or=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 Bn 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 Bn 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.