Nowadays, the production of hydrogen has received increased attention due to its important industrial applications and to its promising potential as an alternative energy source. The use of hydrogen in fuel cell applications requires a high purity. In this work, hydrogen purification from mixtures that also contain CO2, CO, CH4, and N2 was performed by Pressure Swing Adsorption (PSA) with CuBTC as adsorbent (supplied by KRICT). The equilibrium adsorption of each pure gas was measured and fixed-bed adsorption experiments were carried out. The same column, employed for the fixed-bed breakthrough curves, was used to carry out experiments of a 4-step PSA cycle. A mathematical model of multicomponent adsorption in fixed bed was developed. This model was validated against the results obtained in breakthrough experiments and PSA tests, presenting a good fitting to experimental data. Therefore, this model can be used as a base for the design of optimized PSA cycles.