The investigation of nanomaterials with improved energy storage performance is essential in the development of high energy density supercapacitors. Herein, bismuth manganese oxide (BiMn₂O₅, BMO) nanoparticles were facilely synthesized by a combustion method and used as an electrode material in aqueous and quasi-solid-state asymmetric supercapacitors (ASCs). In a three-electrode system, the BMO electrode exhibited a specific capacitance of 228 F g⁻¹ at a current density of 2 A g⁻¹ in 1 M H₂SO₄ electrolyte. Furthermore, to enhance the performance of the electrode material, the bare electrolyte was modified by redox-additive potassium iodide (KI), and then an improved specific capacitance of 405 F g⁻¹ at 2 A g⁻¹ was obtained. Moreover, the ASC device was fabricated using a gel electrolyte (PVA : H₂SO₄ = 1 : 1) with a small amount of redox-additive KI, which demonstrated the maximum specific capacitance of 206 F g⁻¹ at 1 A g⁻¹. The energy and power densities of the device were found to be 114 W h kg⁻¹ and 0.99 kW kg⁻¹, respectively, at 1 A g⁻¹. The almost stable specific capacitance of the device was obtained until 2500 cycles, indicating the excellent durability of the ASC. To check the viability of the device, twelve parallel connected red color light-emitting diodes were successfully operated with two series connected ASCs, suggesting its good energy storage performance. Furthermore, an electric motor fan was also powered by ASCs. The BMO nanoparticles and redox-additive electrolytes are expected to be economically favorable strategies to enable the high energy storage performance of supercapacitor devices.