The large eddy simulation (LES) is applied to an unconfined swirling flow of an air surrounding a bluff-body having a central jet of air, and the complicated flow field that involves the recirculation and vortex breakdown is investigated. The Smagorinsky model is used as the sub-grid scale model. The results of the present numerical simulation are compared with the experimental data of the mean and stochastic root mean square (RMS) variations of two velocity components. Although the inflow conditions are specified in a simple manner, the obtained numerical results are in a reasonable agreement with the experiments, except for a part of RMS variation values behind the bluff body. The present numerical calculations can successfully reproduce the characteristics of the flow, i.e., an upstream recirculation region established just downstream of the burner plane. Additionally, the flow field is much different by the swirl number and axial velocity of the primary swirling air. Especially the additional recirculation region is established at the more downstream location in the lower swirl number and higher axial velocity of the primary swirling air.