For the purpose of simulating ocean turbulence in the artefact scale in the future, we conducted basic research on DNS (Direct Numerical Simulation) and LES (Large Eddy Simulation) of homogeneous shear turbulence in thermal stratification. Here we focused our attention on the applicability of anisotropic LES turbulence models. Firstly, the known characteristics of the homogeneous shear turbulence were reaffirmed with the DNS results. This fact may validate our numerical simulations. Secondly, the LES models were tested for the Richardson number of 0.2 and the Reynolds number of 25700. The initial Taylor-microscale Reynolds number, which denotes the intensity of initial turbulence, was set to be 22.36. We found that neither the classical Smagorinsky model nor the recently proposed Structure-Function model are able to represent the energy spectra very well at higher wave numbers and that the anisotropic LES models perform better in fitting the DNS data than the isotropic models do. Particularly, SGS (Sub-grid Scale) stresses were simulated well by the Dynamic Two-parameter Mixed model. It is thought that the concept of scale similarity and the consideration of the Leonard and cross terms can elucidate appropriate SGS energy dissipation.