Nonlocal absorption of gold and silver nanostructures is studied with ADE-FDTD method. A Drude-Lorentz model of metal material is discretized and iterative coefficients are deduced in detail. Absorption characteristics of one-, two- and three-dimensional gold and silver nanostructures are studied. It shows that the nonlocal layered films conforms to the equivalent medium theory. In one- and two-dimensional cases, nonlocal absorption peaks are related to the nano scale and have no relation with the material. The nonlocal absorption properties of three-dimensional nanostructures are related to nanoscale, and to material as well. Nonlocal effect of three-dimensional nano structures is the strongest, and the blue shift of the absorption peak is larger. Therefore, three-dimensional gold and silver nano structures are expected to play a role in nano devices.