Using first-principles density functional theory calculations, we investigate adsorption properties and the diffusion mechanism of a Li atom on hydrogenated single-layer α- and β-silicene on a Ag(111) surface. It is found that a Li atom binds strongly on the surfaces of both α- and β-silicene, and it forms an ionic bond through the transfer of charge from the adsorbed atom to the surface. The binding energies of a Li atom on these surfaces are very similar. However, the diffusion barrier of a Li atom on H-α-Si is much higher than that on H-β-Si. The energy surface calculations show that a Li atom does not prefer to bind in the vicinity of the hydrogenated upper-Si atoms. Strong interaction between Li atoms and hydrogenated silicene phases and low diffusion barriers show that α- and β-silicene are promising platforms for Li-storage applications.