Abstract A comprehensive multi-phase combustion model has been developed to study the physiochemical processes involved in the combustion of ammonium dinitramide (ADN). The numerical model is based on the conservation equations of mass, species concentration, and energy, and takes into account finite-rate chemical kinetics in both condensed and gas phases. Based on an extensive review of the literature on ADN thermal decomposition, three global decomposition reactions in the condensed phase of ADN are included. A detailed chemical kinetics scheme involving 34 species and 165 reactions is employed in the gas phase. Detailed combustion-wave structures and burning rate characteristics of ADN are described. The optimized gas-phase kinetics mechanism was able to predict the multi-stage flame structure. Good agreements between the predicted and measured profiles of temperature and species mole fractions were obtained at different pressures. Reasonable agreements between calculated and measured values of propellant burning rates and surface temperatures were obtained over a broad range of pressure from 0.7 to 350 atm. The burning rate increases with pressure, except in the mid range of ∼60–100 atm. The coupled condensed- and gas-phase analysis employed in the current model is able to capture this irregular/unstable combustion behavior in the mid range, where the burning rate decreases with the increase in pressure.