Flow inside a scramjet combustor is high Re, turbulent and owing to compressibility and heat release, exhibits strong density variations. Predicting the performance of scramjet combustor requires accurate statistical properties of the flow field. Large eddy simulation (LES) technique makes the computation of turbulent flows feasible with the current computational resources, but requires modeling of the small scale turbulent motions, referred to as subgrid-scale(SGS) modeling. Commonly used SGS models for variable density flows use closure expressions borrowed from models developed for incompressible/constant-density flows. In these models, the density filtered velocity plays the role of the incompressible velocity and comes into the picture because compressible Navier Stokes solvers typically compute conserved variables. However, in the presence of strong density gradients, the conventionally used SGS models can be deficient due to the absence of subgrid-scale effects that arise from interactions between the variable-density fluid and the flow pressure gradients. In this paper, we adapt the stretched-vortex subgrid-scale model (SVM) to variable-density turbulent flows. The proposed model utilizes the filtered velocity field and also accounts for vorticity generation by baroclinic torque within the framework of stretched-spiral subgrid-scale vortices. It is the physical space framework of the stretched-spiral vortex that allows for ready inclusion of variable density physics. The modified model predicts larger SGS kinetic energy and SGS dissipation in regions with strong density gradients.