This paper presents the simulation of complex separation flows over a modern fighter model at high angle of attack by using an unstructured/hybrid grid based Detached Eddy Simulation (DES) solver with an adaptive dissipation second-order hybrid scheme. Simulation results, including the complex vortex structures, as well as vortex breakdown phenomenon and the overall aerodynamic performance, are analyzed and compared with experimental data and unsteady Reynolds-Averaged Navier-Stokes (URANS) results, which indicates that with the DES solver, clearer vortical flow structures are captured and more accurate aerodynamic coefficients are obtained. The unsteady properties of DES flow field are investigated in detail by correlation coefficient analysis, power spectral density (PSD) analysis and proper orthogonal decomposition (POD) analysis, which indicates that the spiral motion of the primary vortex on the leeward side of the aircraft model is highly nonlinear and dominates the flow field. Through the comparisons of flow topology and pressure distributions with URANS results, the reason why higher and more accurate lift can be obtained by DES is discussed. Overall, these results show the potential capability of present DES solver in industrial applications.