Exhausts of airship fabric bag in the stratosphere such as hydrogen which can be used for fuels by using catalytic combustion method. This can save the extra fuels used in the power system. Pd/γ- Al₂O₃ catalyst was prepared in this work by impregnation method and the H₂ catalytic combustion reaction kinetic was investigated between the pressure of 3.6 kPa and 101.3 kPa. The effects of temperature, pressure and gas composition ratio were studied in the paper. According to the experiment results, the increase of temperature increases the H₂ conversion. The parameter pressure has a positive effect on H₂ reaction kinetics and low concentration of H₂ in mixtures shows better performance. The dependence of temperature on H₂ reaction rate becomes more sensitive in high pressure.