The heat generated in a high-temperature gas-cooled reactor can be used to drive the iodine-sulfur cycle to produce hydrogen. However, the sulfuric acid decomposition step requires a sophisticated sulfuric acid decomposer to increase the decomposition rate. The decomposition of sulfuric acid mainly occurs in the catalytic zone, and the optimization of its structure is very important for increasing the decomposition rate. This study focuses on the structural design of the catalytic zone of the sulfuric acid decomposer unit. The structure with double inner tubes is designed to analyze the influence of the inner tube heat transfer area and the catalytic volume of the annulus region on the decomposition rate. The species transport model is used to predict the proportion of products followed by analysis of the key factors affecting the decomposition rate of the catalytic domain. The results reveal that the new design attains the decomposition temperature requirements and increases the fluid velocity of the inner tube. This in turn promotes the heat transfer effect. The decomposition rate is negatively correlated with the flow rate. Nonetheless, a structure with double inner tubes which have the same total area of inner tube as a structure with a single inner tube has a better optimization effect than a structure which has the same annulus catalytic volume as a structure with single inner tube. It increases the decomposition rate by up to 6.1% while a structure which has the same annulus catalytic volume as a structure with a single inner tube does the same by up to 1.7%. The decomposition rate can be maintained at a relatively high level when the inlet velocity of the current structural design is about 0.2 m/s. This study provides a reference for the engineering design of sulfuric acid decomposer based on the heat exchange area and catalytic volume.