The diffusion behavior of lithium in the α-Sn and β-Sn were investigated using density function theory (DFT). The diffusion barrier of single lithium atom in the α-Sn is 0.21 eV, which shows a little change as another lithium atom was next to it. However, the barrier is 0.39eV for lithium in the β-Sn and the lithium tend to bond together when more lithium atoms appear. The different behavior of diffusion barriers are attributed to a different binding energy of Li-Li atoms in Sn with the different crystal structures. The α-Sn used as an anode material for lithium ion batteries is preferable to β-Sn for the fast diffusion of lithium.