A low-cost, non-toxic nanocomposite of two-dimensional (2D) nanosheets of acid-etched graphitic carbon nitride (TGCN) and one-dimensional (1D) nanorods of zinc oxide (ZnO NRs) is prepared using one-step calcination method. The average size and diameter of ZnO nanorods in TGCN/ZnO (T-ZnO) nanocomposite is reduced to 0.5 and 0.73 times than pristine ZnO NRs, respectively. After the acid-etching process, the size of the T-ZnO nanocomposite is further reduced which enhanced its specific surface area to 16.82 m2/g as compared to pristine ZnO NRs (3.56 m2/g). T-ZnO NRs shows a specific capacitance of 398.47 F/g using 0.5 M H2SO4 which is higher as compared to T-ZnO NRs using 0.5 M Na2SO4 (278.16 F/g) and 6 M KOH (106.10 F/g). Using Electrochemical impedance spectroscopy, diffusion coefficient (D) value 1.85 × 10−11 is obtained for T-ZnO NRs (0.5 M H2SO4). T-ZnO NRs also exhibits a higher specific capacitance of 311.80 F/g at 1 A/g using 0.5 M H2SO4. The nanocomposite shows superior energy density of 97.43 Wh/kg at 750 W/kg of power density. The superior capacitance retention (>95 %) and stable coulombic efficiency (>80 %) of T-ZnO NRs enables the nanocomposite for practical applications in energy storage devices. The electric double layer (EDL) and pseudocapacitive (PC) contribution of 6.04 % and 93.96 % to the total specific capacitance of T-ZnO NRs is evaluated using Trasatti method. The capacitive and diffusion-controlled contribution is also investigated for T-ZnO NRs using Dunn's method. The practical aspect of a supercapacitor using leakage current and self-discharge is also tested for the T-ZnO NRs. T-ZnO NRs is a promising energy storage material to fill the gap in the ongoing energy crisis.