A model has been developed for the batch and continuous fermentation of Lactococcus lactis strain NZ133. It was observed that the growth kinetics of L. lactis was predominantly influenced by lactose limitation and lactate product inhibition with the growth of this particular strain showing a relatively high sensitivity to lactate inhibition. The Luedeking–Piret equations for growth and for lactate production were successfully incorporated into the model. Parameters for the model were determined based on experimental data using a program developed in Microsoft EXCEL. The values of the key kinetic constants were: maximum specific growth rate ( μ max), 1.10 h −1; growth associated constant for lactate production ( α), 0.932 g g −1; non-growth associated constant for lactate production ( β), 3.02 g g −1 h −1; average lactate yield based on lactose ( Y p/ s ), 0.93 g g −1. When compared with batch experimental data, the model provided good predictions for growth, lactose utilisation and lactate production profiles on media with initial lactose concentrations ranging from 20 to 100 g l −1. The model also provided good prediction of continuous culture data on medium with an initial lactose concentration of 40 g l −1.