A stabilized finite element formulation for the computation of turbulent reacting flows and NOx emission is presented. The method is based on the Streamline-Upwind/Petrov–Galerkin (SUPG) and Pressure-Stabilizing/Petrov-Galerkin (PSPG) formulations, complemented with directionally formulated diffusion for reaction-dominated flows (‘DRDJ’ stabilization). The stabilized formulation is applied to the advection–diffusion–reaction equations governing the turbulent combustion and the NOx emission equations based on the thermal and the N2O pathways. The simulation is carried out for a co-axial burner, with a non-premixed swirling flame. The burner is operated at high pressure to represent the take-off conditions for an aero-engine. The vortical patterns of the swirling flame are analyzed together with the temperature field and flame position. The NOx formation processes are discussed, providing insight into the features of thermal and N2O mechanisms. Copyright © 2010 John Wiley & Sons, Ltd.