Substrates are normally required in the chemical synthesis of graphene to enhance its formation. However, removing substrates in the post purification stage is difficult, during which harsh reagents are used and the substrates are usually consumed undesirably. In this paper, we report that universal sodium carbonate (Na2CO3) particles can effectively promote the construction of well-structured graphene frameworks based on a quick thermal decomposition of fumaric acids. Notably, the Na2CO3 particles are easily separated from graphene through a simple and green method, namely, washing with water at room temperature. Together with the reused characteristic of the recovered Na2CO3 particles, this approach is undoubtedly beneficial to the low-cost and clean synthesis of graphene. Benefiting from the framework structure, the as-synthesized graphene exhibits excellent performance in the supercapacitor. The specific capacitance of the GFs-modified electrode was calculated to be 242 F g−1 at 0.5 A g−1, which was almost twice that of the RGO-modified electrode (134 F g−1). More importantly, the GFs-modified electrode maintained 92.6% retention of its initial specific capacitance (from current density of 0.5 to 16 A g−1), which was much higher than that of 2D graphene-modified electrode.