In order to evaluate the catalytic effects of inorganic acids on the decomposition of ammonium nitrate (AN), the heat releases of decomposition or reaction of pure AN and its mixtures with inorganic acids were analyzed by a heat flux calorimeter C80. Through the experiments, the different reaction mechanisms of AN and its mixtures were analyzed. The chemical reaction kinetic parameters such as reaction order, activation energy and frequency factor were calculated with the C80 experimental results for different samples. Based on these parameters and the thermal runaway models (Semenov and Frank-Kamenestkii model), the self-accelerating decomposition temperatures (SADTs) of AN and its mixtures were calculated and compared. The results show that the mixtures of AN with acid are more unsteady than pure AN. The AN decomposition reaction is catalyzed by acid. The calculated SADTs of AN mixtures with acid are much lower than that of pure AN.