Abstract: A compressible plane jet at Mach 0.9 is numerically studied by large-eddy simulation. The governing equations are discretized by fourth-order spatial and third-order temporal schemes. Five sub-grid-scale (SGS) models, namely, the standard Smagorinsky model (SM), the coherent structure kinetic model (CKM) and the selective mixed-scale model (SMSM), the localized dynamic Smagorinsky model (LDSM), and the coherent-structure Smagorinsky model (CSM), are employed for closure of the sub-grid scale (SGS) terms, respectively, and compared. Proper orthogonal decomposition (POD) method is applied to extract the leading modes of the fluctuating velocity components, i.e., u' in the streamwise, v' in the lateral and w' in the spanwise. The averaged flow fields, dissipation, the instantaneous vortical structures and the coherent structures represented by the leading POD modes, are compared. The leading POD modes of u' are two longitudinal stripes with fracted contours in the turbulent region, representing the multi-scaled flow and the decay of fluctuation strength. The leading modes of v' are a row of ribs with the lateral size growing along the streamwise, while the modes of \left( u', v' \right) are in a circular flow pattern around the ends of the ribs. The circular pattern penetrates both the jet flow and the peripheral flow, representing the flow entrainment. The leading modes of w' are a train of ridges along streamwise. Their positive and negative values represent the spanwise stretching pattern of the coherent structures. In comparison of these five SGS models, the instantaneous multi-scale vortical flow is not effectively predicted by the SM and the CKM, as the small vortical scale is smeared. The POD modes are found to be sensitive to the sub-grid dissipation, since the valley regions of the mode of u' coincide with the peak dissipation regions predicted by the CKM. The circular flow pattern is also not clearly predicted by the CKM. Neither the ridge pattern of the mode of w' is predicted by the SM. On the other hand, the multi-scales turbulent flow and the flow patterns of POD modes are well predicted by the CSM, the SMSM, and the LDSM, in which the CSM is computationally more efficient.