Li-ion hybrid supercapacitors (LIHSs) have recently attracted increasing attention as a new and promising energy storage device. However, it is still a great challenge to construct novel LIHSs with high-performance due to the majority of battery-type anodes retaining the sluggish kinetics of Li-ion storage and most capacitor-type cathodes with low specific capacitance. To solve this problem, 3D graphene-wrapped MoO3 nanobelt foam with the unique porous network structure has been designed and prepared as anode material, which delivers high capacity, improved rate performance, and enhanced cycle stability. First-principles calculation reveals that the combination of graphene dramatically reduces the diffusion energy barrier of Li+ adsorbed on the surface of MoO3 nanobelt, thus improving its electrochemical performance. Furthermore, 3D graphene-wrapped polyaniline nanotube foam derived carbon is employed as a new type of capacitor-type cathode, demonstrating high specific capacitance, good rate performance, and long cycle stability. Benefiting from these two graphene foam-enhanced materials, the constructed LIHSs show a wide operating voltage range (3.8 V), a long stable cycle life (90% capacity retention after 3000 cycles), a high energy density (128.3 Wh·kg-1), and a high power density (13.5 kW·kg-1). These encouraging performances indicate that the obtained LIHSs may have promising prospect as next-generation energy-storage devices.