A hierarchical structure consisting of Ni-Co hydroxide nanopetals (NCHPs) grown on a thin free-standing graphene petal foam (GPF) has been designed and fabricated by a two-step process for pseudocapacitive electrode applications. The mechanical behavior of GPFs has been, for the first time to our knowledge, quantitatively measured from in situ scanning electron microscope characterization of the petal foams during in-plane compression and bending processes. The Young's modulus of a typical GPF is 3.42 GPa, indicating its outstanding mechanical robustness as a nanotemplate. The GPF/NCHP electrodes exhibit volumetric capacitances as high as 765 F cm(-3), equivalent to an areal capacitance of 15.3 F cm(-2) and high rate capability. To assess practical functionality, two-terminal asymmetric solid-state supercapacitors with 3D GPF/NCHPs as positive electrodes are fabricated and shown to exhibit outstanding energy and power densities, with maximum average energy density of approximate to 10 mWh cm(-3) and maximum power density of approximate to 3 W cm(-3), high rate capability (a capacitance retention of approximate to 60% at 100 mA cm(-2)), and excellent long-term cyclic stability (full capacitance retention over 15 000 cycles).