A numerical solution of the pseudo-steady state governing equations on the basis of the Langmuir-Hinshelwood type rate equation was obtained by the approximate finite difference method in packed bed reactors for gas-solid reaction system. It was proved that the numerical method has good accuracy compared with the strict .solution in the special case that the reaction rate can be represented by the first-order kinetics in terms of gaseous reactants and the effectiveness factor is unity during the reaction. The numerical method is proposed to predict the transient of exit-gas compositions of a packed bed reactor used for gas-solid reaction systems. The exit-gas composition can be predicted from the conversion data of a single particle with varying reaction time. The presentenced can be easily applied to the systems involving adsorptive gaseous reactants and complex reaction behavior with structural changes of particles.