Results obtained using conditional moment closure (CMC) approach to modeling a lifted turbulent hydrogen flame are presented. Predictions are based on k-ε-g turbulent closure, a 23-step chemical mechanism and a radially averaged CMC model. The objectives are to find out how radially averaged CMC can represent a lifted flame and which mechanism of flame stabilization can be described by this modeling method. As a first stage of the study of multi-dimensional CMC for large eddy simulation (LES) of the lifted turbulent flames, the effect of turbulence upon combustion is included, the high-order compact finite- difference scheme (Padé) is used and previously developed characteristic-wave-based boundary conditions for multi- component perfect gas mixtures are here extended to their conditional forms but the heat release due to combustion is not part of the turbulent calculations. Attention is focused to the lift-off region of the flame which is commonly considered as a cold flow. Comparison with published experimental data and the computational results shows that the lift-off height can be accurately determined, and Favre averaged radial profiles of temperature and species mole fractions are also reasonably well predicted. Some of the current flame stabilization mechanisms are discussed.