The aim of this work was to explore the possibility of using a Cu-exchanged zeolitic volcanic tuff (which is natural and easy to prepare and apply) for the preparation of a new low-cost carbon paste amperometric sensor for H2O2 detection. The properties of the zeolitic volcanic tuff were determined using chemical analysis, energy-dispersive X-ray spectroscopy, the specific surface area, electron microscopy, X-ray diffraction spectroscopy, and Fourier-transform infrared spectroscopy. The sensor was successfully built and operates at pH 7, at an applied potential of −150 mV Ag/AgCl/KClsat, presenting a sensitivity of 0.87 mA M−1, a detection limit of 10 µM and a linear domain up to 30 mM H2O2. These good electroanalytic parameters for H2O2 detection (a low detection limit and high sensitivity) support the possibility of using these sensors for the detection of many analytes in environmental, food and medical applications.