Metamaterial with negative permittivity and permeability is studied by means of computer simulations. We analyze the electromagnetic response of nanostructured metamaterials to evanescent waves at optical frequency via the finite-difference time-domain simulations on parallel computer. Effects of the nanostructure on dielectric and magnetic properties are taken into account by introducing the Drude-Lorentz model in the materials dispersion. Size effect on the dispersion is examined by comparing the model with that of a noble metal particle. A re-focusing and an amplification of the evanescent waves propagating through a metamaterial, consisting of metal slabs/vacuum stacking, are demonstrated for the frequency range at 614-744 THz. By properly treating the materials dispersion, we show that the nanostructured metamaterial may behave as a left-handed material in the optical range. [doi:10.2320/matertrans.MC200822]