Referring to the construction of shear stress transport-improved delayed detached-eddy simulation (SST-IDDES) method, a variant of IDDES method based on the Speziale-Sarkar-Gatski/Launder-Reece-Rodi (SSG/LRR)-ω Reynolds-stress model (RSM) as Reynolds-averaged Navier-Stokes (RANS) background model, is proposed. Through combining high-order weighted compact nonlinear scheme (WCNS), the SSG/LRR-IDDES method is applied to three aeronautic cases and compared with traditional methods:SST-unsteady Reynolds-averaged Navier-Stokes (URANS), SSG/LRR-URANS, and SST-IDDES. To verify the SSG/LRR-IDDES method in simulating airfoil stalled flow, NACA0012 airfoil is adopted separately at attack angles of 17°, 45° and 60°. At the attack angle of 17°, SST-URANS, SSG/LRR-URANS, and SST-IDDES methods each predict a higher lift coefficient than the experimental data, while the SSG/LRR-IDDES method obtains a better lift coefficient result and a higher fidelity vortical flow structure. It indicates that the RSM can improve the prediction of RANS-mode for pressure-induced separations on airfoil surfaces in detached-eddy simulation. At the attack angles of 45° and 60°, the SSG/LRR-IDDES method captures the massively separated flow with three-dimensional vortical structures and obtains a good result, which is the same as that from the traditional SST-IDDES method. To indicate the improvement of the SSG/LRR-IDDES method in simulating airfoil trailing edge separation, NACA4412 airfoil is adopted. At the attack angle of 12° (maximum lift), the trailing edge separation is mainly induced by pressure gradient. The SSG/LRR-IDDES method can predict the separation process reasonably and obtains a good lift coefficient and location of separation compared with experimental results. However, none of other methods can predict trailing edge separation. It confirms that when RSM is adopted as RANS background model in detached-eddy simulation, the ability to predict pressure-induced separation on airfoil surface is improved. For further verifying the SSG/LRR-IDDES method for simulating three-dimensional separated flow, blunt-edge deltawing at the attack angle of 24.6° is adopted. At this attack angle, the primary vortex will break, which is difficult to predict by using the SST-URANS method. For the SSG/LRR-URANS method, it predicts the vortex breakdown successfully, but the breakdown process does not show any significant unsteady characteristic. The SST-IDDES and the SSG/LRR-IDDES methods both predict a significant unsteady vortex breakdown. But in terms of the accuracy of surface pressure and the fidelity of unsteady flow, the result obtained by the SSG/LRR-IDDES method is better than by the SST-IDDES method.