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DFT calculations were used to study the quantum capacitance of pure, B/Al/Si/N/P-doped, and defective γ-graphyne. Due to the direct relationship between capacitance and electronic states around the Fermi level, structures' electronic properties were evaluated by DOS plots. The results of integrated specific quantum capacitance in the range of water stability potential show an improvement of capacity in each p and n-type doping. The calculated cohesive energies of doped structures reflect the stability enhancement. Also, the stability/capacitance of single and double vacancies in two distinct positions (sp and sp2) were examined. The results illustrate stability retention and quantum capacitance improvement of these defective structures. Among the doped structures, the maximum quantum capacitance is 2251.10 F/gr belonging to the aluminum doped structure (in the sp position). For the defective structures, the maximum quantum capacitance is 4221.69 F/gr belonging to removing two sp carbon atoms. These quantum capacitances significantly improved compared to the pristine structure (1216.87 F/gr) and many other structures. These stunning results can contribute to the design of appropriate structures as electrode materials for high-efficiency supercapacitors. [ABSTRACT FROM AUTHOR]