An adiabatic fixed-bed reactor for the simultaneous production of sulfur and hydrogen by catalytic oxidative decomposition of H2S was simulated using a steady-state one-dimensional heterogeneous reactor model. A nonlinear system of differential equations of the first order, characterized by material balances coupled with the energy ones, was solved by numerical integration with the Euler method. The influences of the reactor inlet temperature (T-IN), molar feeding ratio (O-2/H2S), H2S inlet molar fraction (Z(H2SIN)), and pressure on the adiabatic reactor performances were investigated in terms of H2S conversion, H-2 yield, and SO2 selectivity for the homogeneous and the catalytic systems. The reaction system in the presence of Al2O3-based catalyst was compared to the homogeneous one at the reactor inlet temperature of 873 K, highlighting how the catalyzed system is able to reach the final temperature (139S K) more quickly than the homogeneous one. The variation of T-IN, O-2/H2S, and Z(H2SIN) improved both the H2S conversion and the H-2 yield with the reaching of very high temperatures.