Taking advantage of the multi-walled carbon nanotubes in enhancing electrical conductivity and gas generation, metallic silver/carbon nanotube composite (Ag@CNT) was prepared by a facile approach using green tea extract without calcination or high-temperature treatment to enhance both hydrogen (HER) and oxygen (OER) evolution reactions in acidic media. Various physicochemical methods have been utilized to characterize the synthesized Ag@CNT composite, including thermal analysis (TA), atomic force microscopy (AFM), energy-dispersive X-ray spectroscopy (EDX), scanning electron microscopy (SEM), and powder X-ray diffraction (XRD). The fabricated GC/Ag@CNT modified electrodes have been tested for hydrogen evolution in various supporting electrolytes such as H2SO4, NaOH, and Na2SO4. The electrochemical performance of the Ag@CNT electrocatalyst toward hydrogen production in 0.5 M H2SO4 was compared to both pristine CNT and Ag. Results confirmed that current densities of 10 mA cm−2 at overpotentials of − 0.35, − 0.38, and − 0.46 V (vs. RHE) have been obtained for GC/Ag@CNT, GC/Ag, and GC/CNT, respectively, reflecting the enhanced electrocatalysis for the designed composite. Furthermore, marked decrease in the estimated Tafel slopes for the fabricated GC/Ag@CNT (98 mV dec−1) compared to GC/Ag modified electrode (157 mV dec−1) is consistent with facile electrode kinetics. Electrochemical impedance spectroscopy was also employed to determine hydrogen evolution's charge-transfer resistance (RCt) at the three different surfaces. Finally, hydrogen atom adsorption on silver, CNT, and Ag@CNT surfaces was probed via density-functional theory (DFT) whereas energy profile of hydrogen molecules formation was investigated using the Dmol3 numerical model.