In this work, we report the fabrication of a new 3D graphene foam (GF)/carbon nanotube (CNT) hybrid film with high flexibility and robustness as the ideal support for deposition of large amounts of electrochemically active materials per unit area. To demonstrate the concept, we have deposited MnO2 and polypyrrole (Ppy) on the GF/CNT films and successfully fabricated lightweight and flexible asymmetric supercapacitors (ASCs). These ASCs assembled from GF/CNT/MnO2 and GF/CNT/Ppy hybrid films with high loading of electroactive materials in an aqueous electrolyte are able to function with an output voltage of 1.6 V, and deliver high energy/power density (22.8 W h kg−1 at 860 W kg−1 and 2.7 kW kg−1 at 6.2 W h kg−1). The rate performance can be further improved with less loading of electroactive materials (10.3 kW kg−1 at 10.9 W h kg−1). The ASCs demonstrate remarkable cycling stability (capacitance retention of 90.2–83.5% after 10 000 cycles), which is among the best reported for ASCs with both electrodes made of non-carbon electroactive materials. Also the ASCs are able to perfectly retain their electrochemical performance at different bending angles. These ASCs demonstrate great potential as power sources for flexible and lightweight electronic devices.