The fixed-bed catalytic reactors with periodic flow-reversal operation are used to oxidize sulfur dioxide, specially that in the exhausted gas from the non-ferrous metal industry. A one-dimensional two-phase unsteady-state model describing this reactor is derived carefully from the mass conservation of sulfur dioxide and the heat for each phase. The Crank-Nicolson predictor-corrector method on a non-uniform spatial grid is used in solving the derived partial differential equations. The prime feature of the numerical method is that it is of the second-order accuracy both in time and in space. The two-way linked list is selected to store the temperature and concentration in the node points for adapting the change of the node number. Thus the computation accuracy and speed are improved remarkably. Numerical simulation of sulfur dioxide oxidation over vanadium catalysts in a small reactor is presented as an example. Numerical results showed that autothermal oxidation of low concentration sulfur dioxide is feasible. The results are compared with experimental data, The parameter sensitivity is carried out carefully for the mathematical model. Different influences (bed length, gas velocity of bed, initial bed temperature, feed concentration and cycle time) on maximum gas temperature and average conversion, etc., are obtained.