The results of investigation of the kinetics of barium ions precipitation by means of crystalline ammonium sulfate addition in a reaction-crystallization process have been presented. The experiments were performed in a continuous laboratory DTM crystallizer with inner circulation of suspension forced by a liquid jet-pump device generating ascending flow of medium in a mixing chamber. The influence of barium chloride concentration in a feeding solution on the crystal size distribution of barium sulfate product and on its reaction-crystallization kinetics were investigated. Nucleation and crystal growth rates were elaborated on the basis of the kinetic model of the MSMPR crystallizer, in two versions: a simplified one - making assumption that in the BaSO4 crystals population a size-independent growth (SIG) is fulfilled, and the enhanced one, incorporating the size dependent growth (SDG) phenomena observed in a real system. Rojkowski exponential SDG kinetic model was recognized as the practical design equation which is fitted the best to the experimental data in a whole L range tested. Both test data and the kinetic expressions with their parameter values can be practically utilized for the improvement of constructions of liquid jet-pump DTM crystallizers, recommended for complex, coupled processes of precipitation and crystallization of sparingly soluble salts.