A zero-equation sub-grid scale (SGS) model with a variable eddy-viscosity coefficient Cμ is developed for large-eddy simulation. Since Cμ is evaluated based on the resolved shear and vorticity parameters accompanied by the hybrid time scale Tt (combination of dynamic and Kolmogorov time scales), it is sensitized to non-equilibrium flows, preserving the anisotropic characteristics of turbulence. The current model accounts for the SGS kinetic energy with ksgs=Cμ [Formula presented](Δ¯S¯)2 and guarantees the positivity in the energy components. Unlike the original Smagorinsky model, the present SGS model does not need any ad-hoc damping function (Cμ acts as a natural damping function as the wall is approached) or averaging/clipping of the model coefficient for numerical stabilization as required by the dynamic Smagorinsky model (DSM). The model is validated against well-documented flow cases, yielding predictions in good agreement with the direct numerical simulation (DNS) and experimental data. Comparisons indicate some advantages of the new model over the DSM; the current model needs only a single-filtering operation that recovers the numerical stability and computational effort to a greater extent.