Active control of the growth of broiler chickens and pigs has potential benefits for farmers in terms of improved production efficiency, as well as for animal welfare in terms of improved leg health in broiler chickens. In this work, a differential recurrent neural network (DRNN) was identified from experimental data to represent animal growth using a nonlinear system identification algorithm. The DRNN model was then used as the internal model for nonlinear model predictive control (NMPC) to achieve a group of desired growth curves. The experimental results demonstrated that the DRNN model captured the underlying dynamics of the broiler and pig growth process reasonably well. The DRNN based NMPC was able to specify feed intakes in real time so that the broiler and pig weights accurately followed the desired growth curves ranging from −12% to +12% and −20% to +20% of the standard curve for broiler chickens and pigs, respectively. The overall mean relative error between the desired and achieved broiler or pig weight was 1.8% for the period from day 12 to day 51 and 10.5% for the period from week 5 to week 21, respectively.