Phosphogypsum (PG) as a low-cost calcium resource was used to prepare nano-CaCO3 in a three-phase system by reactions. Based on the population balance equation, nano-CaCO3 crystal nucleation and growth model in the gas (CO2)-liquid (NH3 H2O)-solid (CaSO4) three-phase system was established. The crystallization kinetic model of nano-CaCO3 in CO2-NH3.H2O-CaSO4 reactions system was experimental developed over an optimized temperature range of 20-40 degrees C and CO2 flow rate range of 138251 ml/min as rCacO(3) = K-n 32 pi M-2 gamma(3) /3R(3)rho T-2(3 )(C - C*)(0.8 )/[ln(C/C*)](3 )+pi rho/3MK(g)(3)K(n) (C-C*)(2)t(3), where nano-CaCO3 nucleation rate constant was k(n) = 6.24 x 10(19) exp (-15940/RT) and nano-CaCO3 growth rate constant was k(g) = 0.79 exp (-47650/RT) respectively. Research indicated that nucleation rates and growth rates both increased with the increasing of temperature and CO32- ion concentration. And crystal growth was dependent on temperature more than that of nucleation process because the activation energy of CaCO3 growth was bigger than that of CaCO3 nucleation. Decreasing the reaction temperature and CO2 flow rate was more beneficial for producing nano-size CaCO3 because of the lower CaCO3 growth rates. The deduced kinetic equation could briefly predict the average particle sizes of nano-CaCO3. (C) 2018 Elsevier B.V. All rights reserved.