Cobalt-manganese-nickel oxalates micropolyhedrons were successfully fabricated by a room temperature chemical co-precipitation method. Interestingly, the Co0.5Mn0.4Ni0.1C2O4*nH2O micropolyhedrons and graphene nanosheets have been successfully applied as the positive and negative electrode materials (a battery type Faradaic electrode and a capacitive electrode, respectively) for flexible solid-state asymmetric supercapacitors. More importantly, the as-assembled device achieved a maximum energy density of 0.46 mWh·cm(-3), a decent result among devices with similar structures. The as-assembled device showed good flexibility, functioning well under both normal and bent conditions (0°-180°). The resulting device showed little performance decay even after 6000 cycles, which rendered the Co0.5Mn0.4Ni0.1C2O4*nH2O//Graphene device configuration a promising candidate for high-performance flexible solid-state asymmetric supercapacitors in the field of high-energy-density energy storage devices.