Platinum (Pt)-decorated graphene-based carbon composite electrodes with controlled dimensionality were successfully fabricated via core-shell electrospinning/electrospraying techniques. In this process, multilayer graphene sheets were converted into the three different forms, fiber, sphere, and foam, by tailoring the polymer concentration, molecular weight of polymer, and applied voltage. As polymer concentration increased, continuous fibers were produced, whereas decreasing polymer concentration caused the formation of graphene-based foam. In addition, the reduction in polymer molecular weight in electrospun solution led to the creation of three-dimensional (3D) spherical structures. In this work, graphene-based foam was produced for the first time by utilizing core-shell electrospraying technology instead of available chemical vapor deposition techniques. The effect of morphologies and dimensions of carbonized graphene-based carbon electrodes on its electrochemical behavior was investigated by cyclic voltammetry and galvanostatic charge-discharge methods. Among the three different electrodes, Pt-supported 3D graphene-based spheres showed the highest specific capacitance of 118 F/g at a scan rate of 1 mV/s owing to the homogeneous decoration of Pt particles with a small diameter of 4 nm on the surface. After 1000 cycles of charging-discharging, Pt-decorated graphene-based structures showed high cyclic stability and retention of capacitance, indicating their potential as high-performance electrodes for energy storage devices.