Graphdiyne (GD) is a new carbon allotrope, consisting of an sp- and sp2-hybridized carbon network. In this work, density functional theory calculations are carried out to investigate the adsorption and diffusion of lithium (Li) atoms on GD monolayers, and the results are compared with those for graphyne and graphene monolayers. High-capacity Li storage, as LiC3, has been predicted, and the preferred adsorption sites for Li have been identified computationally. Moreover, it is found that Li can easily diffuse on the GD monolayer with moderate barriers of 0.18 to 0.84 eV. The predicted high capacity and mobility indicate that GD may offer excellent performance as the anode of lithium batteries.