The development of more efficient energy conversion and storage devices remains a pressing need in attempting to achieve a high level of market penetration of electric vehicles and use of intermittent renewable energy sources such as wind and solar energy. Current lithium-ion batteries, although an attractive energy storage device, have limited charge capacity that diminishes rapidly at high charge/discharge rates. We have shown previously that a Si-graphene composite integrated into a 3-dimensional, conducting graphitic network offers high structural and cycling stability and substantially higher charge capacity as an anode material than graphite. However, the composite suffers from the problem of diminishing charge capacity during high current operations. Here, we report a facile microscopic engineering strategy to enhance the Li ion transport in graphene sheets, which could be utilized as a platform to create high-power battery materials. When used with Si nanoparticles to form a Si-graphene composite and integrating the composite into a 3-dimensional graphitic network to form a self-supporting electrode paper, the electrode exhibits an outstanding energy density-power density combination, without compromising the usable lifetime and mechanical flexibility. The power capability was found to be comparable to supercapacitors but with a much higher energy density. For example, a charge capacity of over 1000 mAh/g was achieved at a discharge rate of 8 A/g. Structural characterization by high resolution electron microscopy and impedance measurements provided evidence that relates the structural properties to the Li ion diffusivity for this material, which can bridge the performance disparity between batteries with high energy density and capacitors with high power density.