A novel model of bulk AIN crystal grow th by the sublimation technique is developed. The model takes into account both diffusive and convective transport of gaseous Al and N-2 and the kinetic limitation of nitrogen adsorption/desorption on AIN surfaces. The maximum growth rate is found to be controlled by joint effect of enhancement of the convective species transport in a nearly stoichiometric vapor phase and of the suppression of nitrogen incorporation into the crystal due to low N-2 sticking probability. The interplay of these effects provides nonmonotonic dependence of the growth rate on pressure. The theoretical predictions agree well with experimental data reported in literature and obtained in this work.