For the purpose of developing swirl combustors with high combustion efficiency and low pollutant emission, a numerical simulation of swirling turbulent flows in a swirl combustor with coaxial jet interactions is performed. A new algebraic Reynolds stress model and the QUICK discretization scheme are utilized in the present calculations. The simulated results of swirling turbulent flows in the combustor for both cases of the coswirl jets and the counterswirl jets are in agreement with the experiment data in terms of the time-averaged gas axial velocity, tangential velocity and static pressure.