Deficiencies of cathode materials severely limit cycling performance and discharge rates of Li batteries. The key problem is that cathode materials must combine multiple properties: high lithium ion intercalation capacity, electrical/ionic conductivity, porosity, and mechanical toughness. Some materials revealed promising characteristics in a subset of these properties, but attaining the entire set of often contrarian characteristics requires new methods of materials engineering. In this paper, we report high surface area 3D composite from reduced graphene oxide loaded with LiFePO4 (LFP) nanoparticles made by layer-by-layer assembly (LBL). High electrical conductivity of the LBL composite is combined with high ionic conductivity, toughness, and low impedance. As a result of such materials properties, reversible lithium storage capacity and Coulombic efficiency were as high as 148 mA h g(-1) and 99%, respectively, after 100 cycles at 1 C. Moreover, these composites enabled unusually high reversible charge-discharge rates up to 160 C with a storage capacity of 56 mA h g(-1), exceeding those of known LFP-based cathodes, some of them by several times while retaining high content of active cathode material. The study demonstrates that LBL-assembled composites enable resolution of difficult materials engineering tasks.