Subgrid-scale (SGS) parameterizations in atmosphere and ocean models are often defined independently in the horizontal and vertical directions because the grid spacing is not the same in these directions (anisotropic grids). In this paper, we introduce a new anisotropic SGS model in large-eddy simulations (LES) of stratified turbulence based on horizontal filtering of the equations of motion. Unlike the common horizontal SGS parameterizations in atmosphere and ocean models, the vertical derivatives of the horizontal SGS fluxes are included in our anisotropic SGS scheme, and therefore the horizontal and vertical SGS dissipation mechanisms are not disconnected in the newly developed model. Our model is tested with two vertical grid spacings and various horizontal resolutions, where the horizontal grid spacing is comparatively larger than that in the vertical. Our anisotropic LES model can successfully reproduce the results of direct numerical simulations, while the computational cost is significantly reduced in the LES. We suggest the new anisotropic SGS model as an alternative to current SGS parameterizations in atmosphere and ocean models, in which the schemes for horizontal and vertical scales are often decoupled. The new SGS scheme may improve the dissipative performance of atmosphere and ocean models without adding any backscatter or other energizing terms at small horizontal scales.