The ground state equilibrium bond length, harmonic vibrational frequency, and dissociation energy of AlX (X=3d,4d,5d elements and Lu) dimers are investigated by density functional method B3LYP. The present results are in good agreement with the available experimental and other theoretical values except the dissociation energy of AlCr. The present calculations show that the late transition metal can combine strongly with aluminum compared with the former transition metal. The present calculation also indicates that it is more reasonable to replace La with Lu in the Periodic Table and that the bonding strengths of zinc, cadmium, and mercury with aluminum are very weak.