Direct numerical simulations of a lean premixed turbulent Bunsen flame with hydrogen addition have been performed. We show the results for a case with equivalence ratio of 0.7 and a molar fractional distribution of 40% H2 and 60% CH4. The flamelet-generated manifold technique is used to reduce the chemistry; flamelets with different equivalence ratios and inflow temperature are used to account for stretch effects that are enhanced by preferential diffusion. The three-dimensional simulation clearly shows enhanced burning velocity in regions convex toward the reactants and reduced burning velocity with possible extinction in regions concave toward the reactants. To obtain these effects it was found to be necessary to include two three-dimensional transport equations with essentially different diffusivities. This point is illustrated by comparison of the results with cases in which either a single transport equation was used or two transport equations with minor differences in diffusivities were used. These latter cases incorporated preferential diffusion in the 1D flamelets (and thus in the manifold), but not in the three-dimensional transport. Thus the three-dimensional preferential diffusion effects are shown to enhance curvature and thereby to increase the turbulent burning velocity and reduce the mean flame height. In addition the turbulent burning velocity increases because hydrogen addition leads to a larger laminar flamelet consumption speed. To demonstrate this second effect, results of the cases mentioned above are compared to the results of simulations of the Bunsen flame with 0% hydrogen added to the fuel.