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The turbulent catalytically stabilized combustion of lean hydrogen-air premixtures is investigated numerically in plane channels with platinum-coated isothermal walls. The catalytic wall temperature is 1220 K and the incoming mixture has a mean velocity of 15 m/s and a turbulent kinetic energy of 1.5 m 2 /s 2 . A two-dimensional elliptic model is developed with elementary heterogeneous and homogeneous chemical reactions. The approach is based on a two-layer k-ε model of turbulence, a Favre-average moment closure, a presumed-shape (Gaussian) probability density function for gaseous reactions, and a laminar-like closure for surface reactions. Gaseous combustion is confined close to the catalyst surface due to the diffusional imbalance of the limiting reactant (hydrogen). In addition, the peak rms temperature and species fluctuations are always located outside the extent of the homogeneous reaction zone indicating that thermochemical fluctuations have no significant influence on gaseous combustion. Turbulence is significantly suppressed by gaseous combustion resulting in higher turbulent transport for the leaner mixtures, a successive push of the gaseous reaction zone towards the wall, incomplete combustion, and subsequent catalytic conversion of the leaked fuel. Comparison between turbulent and laminar cases having the same incoming properties shows that turbulence inhibits homogeneous ignition due to increased heat transport away from the near-wall layer.