The Sulfur-Iodine (SI) thermochemical hydrogen production process of a closed cycle consists of three sections, which are so called the Bunsen reaction section, the $H_2SO_4$ decomposition section and the HI decomposition section. To identify the role of oxygen that can be supplied to the Bunsen reaction section via the $H_2SO_4$ decomposition section, Bunsen reactions with a $SO_2,;SO_2-O_2$ mixture and $SO_2-N_2$ mixture as feed gases were carried out using a stirred reactor in the presence of $I_2/H_2O$ mixture. As the results, the amounts of $I_2$ unreacted under the feed of mixture gases were higher than those under the feed of $SO_2$ gas only, and the amount of HI produced was relatively decreased. The results of Bunsen reaction using $SO_2-O_2$ mixture were similar to those using $SO_2-N_2$ mixture. It may be concluded that an oxygen in $SO_2-O_2$ mixture has a role as a carrier gas like a nitrogen in $SO_2-N_2$ mixture. The effects of oxygen were decreased with increasing temperature and decreasing oxygen content in $SO_2-O_2$ mixture.