Cu-catalyzed asymmetric construction of a chiral quaternary center bearing CH3 and CF3 groups was achieved with high to excellent enantioselectivity using our originally developed ligands. The asymmetric conjugate addition of Me3Al to β-CF3-substituted enones and unsaturated ketoesters proceeded efficiently. The use of unsaturated ketoesters gives optically active furanones in high yields with high enantioselectivities. The perfluoroalkyl-substituted enone does not seem to be favorable in the present reaction.