Volumetric energy density is generally considered to be detrimental to the actual application of supercapacitors, which has provoked a range of research work on increasing the packing density of electrodes. Herein, we fabricate a free-standing single-walled carbon nanotubes (SWCNTs)/poly(3,4-ethylenedioxythiophene) polystyrene sulfonate (PEDOT:PSS)/CuHCF nanoparticles (NPs) composite supercapacitor electrodes, with high packing density of 2.67 g cm^-3. The pseudocapacitive CuHCF NPs are decorated onto the SWCNTs/PEDOT:PSS networks and filled in interspace to increase both of packing density and specific capacitances. This hybrid electrode exhibits a series of outstanding performances, such as high electric conductivity, ultrahigh areal and volumetric capacitances (969.8 mF cm^-2 and 775.2 F cm^-3 at scan rate of 5 mV s^-1), long cycle life and superior rate capability. The asymmetric supercapacitor built by using the SWCNTs/PEDOT:PSS/CuHCF film as positive electrode and Mo-doped WO₃/SWCNTs film as negative electrode, can deliver a high energy density of 30.08 Wh L^-1 with a power density of 4.25 kW L^-1 based on the total volume of the device. The approach unveiled in this study could provide important insights to improving the volumetric performance of energy storage devices and help to reach the critical targets for high rate and high power density demand applications.