The practical applications of high capacity metallic Li electrodes is severely hindered by the uncontrollable Li nucleation and growth that lead to poor cycle life and growth of unsafe dendrites. Here we demonstrate the design of porous but robust sponges with Cu nanoparticles and graphene and their applications for enabling Li electrodes with stable cycling under high capacity and high current conditions. We discovered that the Cu nanoparticles decorated on graphene effectively direct the heterogeneous nucleation of Li whereas the graphene frameworks provide ample spaces for confining Li growth. These sponges are able to host at least 60 mAh cm(-2) Li without forming dendrites and allow stable Li plating/stripping with low overpotentials for hundreds of cycles even at a high current of 7 mA cm(-2). The sponges have remarkable mechanical strengths and exhibited minimal structural deformation after aggressive plating/stripping cycles. These superior properties enable Li metal batteries with substantially improved high current cyclic stability and rate performance, as demonstrated with both LiNi0.4Co0.2Mn0.4O2 and LiFePO4 cathodes.