The study of two-stage partial nitrification–anaerobic ammonium oxidation (PN/A) reactors, which are advantageous in engineering applications, still lacks research on process kinetics. Therefore, in this study, the start-up performance and process kinetics of a two-stage PN/A reactor were evaluated by controlling the reaction conditions, for which the two reactors were inoculated with sludge, incubated separately, and then operated in tandem. Increasing the ammonia load of the reactor during the 60 d stabilization period resulted in a nitrogen accumulation rate of 96.93% and a [NO2−-N]Eff/[NH4+-N]Eff ratio of 1.33, which is close to the theoretical value of 1.32. Successful initiation of the A reactor was achieved after 55 d of operation by inoculating with anammox-activated sludge and granular activated carbon, and the PN and A reactors then successfully operated in combination for 20 d, with an average NH4+-N efficiency of 99.04% and the NH4+-N load of the A reactor showing an “S-shaped” curve. An analysis of the microbial growth kinetic models indicated that the removal of NH4+-N could be successfully described by the logistic, modified logistic, modified Gompertz, and modified Boltzmann models. A strong association between the model and the dependent variable was observed. The process kinetic analysis showed that the removal of NH4+-N from reactor A could be simulated under steady-state conditions, using the Grau second-order model. The parameters obtained from the model analysis are expected to help predict the denitrification performance of the reactor, facilitate operational management and control, and thus provide a promising research basis for the introduction of automated control systems.