We perform a density functional study on the adsorption and diffusion of Li atoms on silicene sheet and zigzag nanoribbons. Our results show that the diffusion energy barrier of Li adatoms on silicene sheet is 0.25 eV, which is much lower than on graphene and Si bulk. The diffusion barriers along the axis of zigzag silicene nanoribbon range from 0.1 to0.25 eV due to an edge effect, while the diffusion energy barrier is about 0.5 eV for a Li adatom to enter into a silicene nanoribbon. Our calculations indicate that using silicene nanoribbons as anodes is favorable for a Li-ion battery. We perform a density functional study on the adsorption and diffusion of Li atoms on silicene sheet and zigzag nanoribbons. Our results show that the diffusion energy barrier of Li adatoms on silicene sheet is 0.25 eV, which is much lower than on graphene and Si bulk. The diffusion barriers along the axis of zigzag silicene nanoribbon range from 0.1 to 0.25 eV due to an edge effect, while the diffusion energy barrier is about 0.5 eV for a Li adatom to enter into a silicene nanoribbon. Our calculations indicate that using silicene nanoribbons as anodes is favorable for a Li-ion battery.