Novel cluster anions Li2F- and Li6F- with alkalide character have been studied in the present paper. In contrast to a typical neutral alkalide, Li2F- contains a F- anion instead of the neutral ligand and forms an alkalide anion F-Li+Li-. In addition to a F- anion ligand, Li6F- contains a Li-3(+) superalkali cation instead of the alkali metal cation and a Li-3(-) superalkali anion instead of the alkali metal anion, and this alkalide anion can be denoted by F-Li3+Li3-, which is supported by NBO charge results. The results indicate that the F- anion can polarize not only the Li atom but also the Li-3 superalkali to form alkalide anions with excess electrons. For Li2F-, two linear structures ((1)Sigma(+) and (3)Sigma(+) states) are obtained. For Li6F-, the structure of the (1)A(1) state is a trigonal antiprism capped by the F-anion with C-3 upsilon symmetry, while the structure of the (7)A' state is a slightly distorted trigonal antiprism with C-s symmetry. Due to the excess electrons on the alkali metal and superalkali anions (Li-and Li-3(-)), the alkalide anions Li2F- and Li6F- have large first hyperpolarizabilities (beta(0) = 1.116 x 10(4)-1.764 x 10(5) au). For the spin multiplicity effect on electric properties, in these two alkalide anions, the values of the static electric properties, especially the first hyperpolarizabilities, of the high spin states are larger than the corresponding values of the low spin states. For the substitution effect of superalkali atoms, in the two singlet states, as the Li-3 superalkalis substitute the Li atoms, the value of the mean of polarizability increases, while the values of dipole moment and the first hyperpolarizability decrease.