Numerical calculations of the flow, mixing and combustion in the turbulent swirling flame in a tube were conducted based on the density-weighted Reynolds-stress/flux equation model. Computed axial and tangential velocity components, temperature and species concentration were compared with experimental ones. Swirl effects were investigated by comparing the results of swirling and nonswirling conditions. Computations could predict the retardation of the turbulent mixing due to swirl observed in the experiment. Effects of swirl on the flow, mixing and combustion were interpreted. The importance of two types of the negative production terms, one including the swirl velocity and the other the interaction between density fluctuation and swirl-induced pressure gradient, was emphasized.