Special quasi-random structures (SQSs) with 32 atoms have been generated to model appropriate supercell structure of pseudo-binary random L1(2)-Al-3(Sc0.5TM0.5) (TM = Y, Ti, Zr, Hf, V, Nb and Ta) alloys. The optimized lattice parameters were in good agreement with the experimental data, and the obtained formation energies showed that all L1(2)-Al-3(Sc0.5TM0.5) alloys were stable from energetic point of view. As the atomic radius of substitution elements TM in the same Period decreased, the values of C (12) and C (44) for L1(2)-Al-3(Sc0.5TM0.5) alloys exhibited an overall tendency of increase, implying an enhanced Poisson effect and larger resistance to {100} aOE (c) 001 > shear. The elastic isotropy of L1(2)-Al-3(Sc0.5TM0.5) alloys was overall lowered and the ductility could be improved. The calculated electronic structure demonstrated that below the Fermi level the hybridization of transition-metal d states with Al p states was reduced with decreasing of atomic radius of substitution elements TM in the same Period, which uncovered underlying mechanism for stability and elastic properties of L1(2)-Al-3(Sc0.5TM0.5) alloys.