The double diffusive convection between two parallel plates is numerically studied for a series of parameters. The flow is driven by the salinity difference and stabilised by the thermal field. Our simulations are directly compared with experiments by Hage & Tilgner (Phys. Fluids, vol. 22, 2010, 076603) for several sets of parameters and reasonable agreement is found. This, in particular, holds for the salinity flux and its dependence on the salinity Rayleigh number. Salt fingers are present in all simulations and extend through the entire height. The thermal Rayleigh number seems to have a minor influence on the salinity flux but affects the Reynolds number and the morphology of the flow. In addition to the numerical calculation, we apply the Grossmann–Lohse theory for Rayleigh–Bénard flow to the present problem without introducing any new coefficients. The theory successfully predicts the salinity flux both with respect to the scaling and even with respect to the absolute value for the numerical and experimental results.