The molecular structures of neutral SinLi (n = 2-8) species and their anions have been studied by means of the higher level of the Gaussian-3 (G3) techniques. The lowest energy structures of these clusters have been reported. The ground-state structures of neutral clusters are "attaching structures", in which the Li atom is bound to Si-n clusters. The ground-state geometries of anions, however, are "substitutional structures", which is derived from Sin+1, by replacing a Si atom with a Li-. The electron affinities of SinLi and Si-n have been presented. The theoretical electron affinities of Si-n are in good agreement with the experiment data. The reliable electron affinities of SinLi are predicted to be 1.87 eV for Si2Li, 2.06 eV for Si3Li, 2.01 eV for Si4Li, 2.61 eV for Si5Li, 2.36 eV for Si6Li, 2.21 eV for Si7Li, and 3.18 eV for Si8Li. The dissociation energies of Li atom from the lowest energy structures of SinLi and Si atom from Si-n clusters have also been estimated respectively to examine relative stabilities.