Exopolysaccharides (EPSs) produced by lactic acid bacteria have been widely studied, but their applications as important functional biopolymers are limited due to the low level of EPS production. In this study, Lactiplantibacillus plantarum HMX2 was shown with high capacity of EPS production with a maximum yield of 556.43 mg/L under the optimized fermentation conditions with 27.57 g/L of soy peptone, 20 g/L of sucrose, 4 % (v/v) of inoculum, the initial medium pH 6.4, and fermentation temperature at 34.5 °C for 10 h. The response surface analysis indicated significant interactions between the fermentation conditions, i.e. the initial medium pH vs. fermentation temperature or soy peptone content, which jointly promoted the EPS production by HMX2. The kinetics models for the bacterial growth, EPS synthesis and sucrose consumption during the fermentation under the optimized conditions were established by using Logistic and Boltzmann models. There were good fitting of the models for the experimental results with the relative errors lower than 15 % and correlation coefficients (R2) of higher than 0.99. The results of this study provide basic theoretical support by modelling the fermentation kinetics for efficient production of the EPS by HMX2 and its potential application in functional foods.