A new flexible all-solid-state asymmetric supercapacitor with very high energy density has been fabricated by adopting a 3D heterogeneous composite based on polyaniline (PANI) and graphene and enlarging its operating voltage window. This novel supercapacitor is based on the 3D molybdenum oxide/graphene aerogel (MoO3/GF) composite as the negative electrode and the sandwich-type PANI decorated 3D porous manganese dioxide/reduced graphene oxide hybrid film (PANI/(MnO2−RGO)/PANI) as the positive electrode material. Polyvinyl alcohol/potassium hydroxide (PVA/KOH) was used as the gel electrolyte. The self-assembled 3D MoO3/GF was synthesized by hydrothermal route followed by heat treatment in a furnace. For the positive electrode, a facile novel 3D MnO2−RGO porous film was first fabricated by vacuum filtration of MnO2 and GO suspension, followed by hydrothermal chemical reduction. Then, PANI nanofibers were grown on top of the hybrid film. The fabrication steps show a facile formation of the 3D sandwich-type PANI/(MnO2−RGO)/PANI porous hybrid film. The asymmetric supercapacitor (MoO3/GF//PANI/(MnO2−RGO)/PANI) showed a high energy density of 51.91 Wh kg−1 at a power density of 0.838 kW kg−1. The asymmetric cells were flexible, and three cells connected in series could illuminate a green-LED for 62 s.