Large Eddy Simulation (LES) has been applied to the calculation of a turbulent hydrogen diffusion flame using a conserved scalar formalism. The Favre filtered Navier-Stokes equations have been closed using the Smagorinsky model and its dynamically calibrated variant For the Favre-filtered mixture fraction transport equation, closure has been obtained through combining the subgrid scale eddy viscosity with :a constant-valued subgrid scale Schmidt number. A dynamically calibrated gradient transport model has also been used, and in a third simulation, the equation for xi is left unclosed in order to compare the effects of the dissipation supplied by the model and that produced by the TVD scheme, needed to ensure the boundedness of the mixture fraction xi. An assumption of equilibrium chemistry has been employed to express the thermochemical variables (temperature, density, and species concentrations) as functions of xi. The effects of fluctuations in the subgrid scales on the resolved scale values of these scalars is accounted for through the use of a presumed shape subgrid probability density function (sgpdf) for xi a beta -function has been used in the present case. Knowledge of the subgrid scale mixture fraction variance is needed to fix the shape of the beta -sgpdf; here a simple; equilibrium model has been employed. The results of the simulations show that LES is capable of producing good agreement with measurements of mean velocity, Reynolds stresses and fluxes. The spreading of the mixture fraction field appears to have been slightly overpredicted in all cases. Though this discrepancy is not large, it has a noticeable effect on the predicted mean thermochemical fields in physical space. When plotted against mixture fraction, however, the predicted mean temperature and species concentrations give much better agreement with measurements, and show the combustion model to be working well in the present case.