The present study addresses numerical simulations of the double-diffusive convection in a turbulent regime. The characteristic concentration and temperature Prandtl numbers (PrC = 700 and PrT = 7) correspond to the typical seawater properties. Here, we applied the Large-Eddy Simulation (LES) approach, with relatively simple subgrid turbulence closures of momentum, concentration, and temperature for the unresolved scales. The wall-resolved LES approach proved to work well on significantly coarser numerical mesh than used in recent Direct Numerical Simulation (DNS) studies of Yang et al. (2016) in the intermediate range of working parameters, 107 ≤ RaC ≤ 109, 0 ≤ RaT ≤ 106, which covers the quasi-Rayleigh-Bénard, fingering, and damping flow regimes. A good agreement between concentration and temperature Nusselt numbers is obtained. The instantaneous Nusselt numbers distribution revealed a significant impact of the imposed strong thermal stratification (RaT = 106) in comparison to the neutral case (RaT = 0).