A numerical simulation is presented of the turbulent flows of coaxial jet interactions in a swirl combustor under different conditions. The simulation is performed by employing the full form of a new algebraic Reynolds stress model (ASM). The calculated gas axial and tangential velocities, static pressure, and turbulent fluctuating velocity are compared with the measured test data and those predicted by the simplified form of the new ASM and the k -epsilon model. It is shown that the predictions by the full form of the new ASM agree with the measured data. The results obtained under different swirl numbers of the outer jet indicate that the interactions between the inner and outer coaxial jets have evident effects on the swirling turbulent flows in the combustor.