Relativistic configuration interaction calculations are carried out to study the electronic spectrum of the AlSb molecule. Potential energy curves of 44 electronic states within 6 eV of energy are constructed. Spectroscopic., Ye) of the low-lying A-S states are computed. The equilibrium bond length and constants (r(e), omega(e), T-e, D-e, mu(e) vibrational frequency of the ground state (X(3)Sigma(-)) of AlSb are estimated to be 2.79 Angstrom and 249 cm(-1), respectively. Effects of the spin-orbit coupling on the spectroscopic properties and potential energy curves of states that correlate with the lowest two dissociation limits are investigated. The computed dissociation energy of the ground-state spin component (X(3)Sigma(0+)(-)) is 1.44 eV. Transition moments of several electric dipole-allowed and spin-forbidden transitions are computed from CI wave functions. Radiative lifetimes of the low-lying excited states of AlSb at the lowest three vibrational levels (v' = 0, 1, 2) are estimated. Transitions from the 3(3)Pi(0+) component to all lower states with DeltaOmega = 0, +/-1 are predicted. At v' = 0, the 3(3)Pi(0+) component has a lifetime of about 1.26 mus. The electronic states of AlSb are also compared with those of isovalent Alp, GaAs, GaSb, and InSb molecules.