The absorption of cosmic ray muons was experimentally demonstrated using the telescope which was proposed in our previous work as a portable detector for high-density materials. The complexity of the muon interaction has pushed researchers to use the simulation program (GEANT) that recently showed some discrepancies with observations at high energy but did not describe the attenuation of all muon spectrum. In this study, the absorption/ attenuation coefficients for different elements, namely lead (Pb), copper (Cu), zinc (Zn) and aluminum (Al) were experimentally determined. The count-rate graphs obtained verified the familiar behavior of the absorbers, which led to the determination of the exact transition depth of the metals and the results were consistent with the properties of the metals in other previous works. The attenuation of cosmic muon in lead was very high in comparison with other metals; therefore, lead can be very easily detected by muon absorption. Our results indicate that the larger the atomic weight of the absorber, the higher the ability of the muon absorber. The determined coefficients reported by this study will be useful for future work for muon tomography and detection techniques.