The recent development of synthesis processes for three-dimensional (3D) graphene-based structures has tended to focus on continuous improvement of porous nanostructures, doping modification during thin-film fabrication, and mechanisms for building 3D architectures. Here, we synthesized novel snowflake-like Si-O/Si-C nanostructures on 3D graphene/Cu foam by one-step low-pressure chemical vapor deposition (CVD). Through systematic micromorphological characterization, it was determined that the formation mechanism of the nanostructures involved the melting of the Cu foam surface and the subsequent condensation of the resulting vapor, 3D growth of graphene through catalysis in the presence of Cu, and finally, nucleation of the Si-O/Si-C nanostructure in the carbon-rich atmosphere. Thus, by tuning the growth temperature and duration, it should be possible to control the nucleation and evolution of such snowflake-like nanostructures with precision. Electrochemical measurements indicated that the snowflake-like nanostructures showed excellent performance as a material for energy storage. The highest specific capacitance of the Si-O/Si-C nanostructures was ~963.2 mF/cm² at a scan rate of 1 mV/s. Further, even after 20, 000 sequential cycles, the electrode retained 94.4% of its capacitance.