Metal-organic frameworks (MOFs) are the attractive materials for energy storage applications because of its distinctive properties like high porosity, structural flexibility, high specific surface area, good stability etc. However, their low conductivity motivates to incorporate with some conductive matrix in a way to produce conductive and porous composite. Herein, we have synthesized a hybrid consisting of porous Cu MOF and conductive graphitic carbon nitride (g-C₃N₄) using a simple stirring process. The formation of Cu-MOF/ g-C₃N₄ composite is further confirmed by XRD, Raman, FTIR, BET and FESEM characterizations. The as derived composite shows very high specific surface area, hierarchical porous morphology and good conductivity, therefore becomes suitable to be used as an active electrode material for supercapacitors. Therefore, the composite is tested in three electrode system using 1M H₂SO₄ aqueous electrolyte for electrochemical measurements. In addition, the surface and diffusion charge highly affect the electrochemical performance of the electrodes. For instance, a high fraction of surface charge contribution suggests the fast electrochemical kinetics and hence shows the ability of the electrode to work at a high charge-discharge rate. From this analysis, it is clearly observed that the Cu-MOF/ g-C₃N₄ composite shows lower specific capacitance at high scan rates due to the contribution of more surface charges. On the other hand, at lower scan rates the composite delivers high specific capacitance due to the dominance of diffusion charges as compared to surface charges. Therefore, this work paves the importance of surface and diffusion charge contribution studies to tune the electrochemical performance of next generation electrode materials of supercapacitors.