To overcome weak poinks of the standard k-${varepsilon}$ turbulence model when applied to complex turbulent flows, various modified models were proposed. But their effects are confined to special flow fields. They have still some problems. Recently, an anisotropic k-${varepsilon}$ turbulence model was also proposed to solve the drawback of the standard k-${varepsilon}$ turbulence model. This study is concentrated on the evaluation of the anisotropic k-${varepsilon}$ turbulence model by the analysis of axisymmetric swirling turbulent flow. Results show that the anisotropic k-${varepsilon}$ turbulence model has scarecely the fundamentally physical mechanism of predicting the swirling structure of flow.