Hydrogen-hydrocarbon blend flames have recently received increased attention as alternative fuels for terrestrial and aerospace power generation applications. The combustion modelling of these composite fuels flames is complex. Turbulence modelling as well is difficult because in the near field region of the jet exit, high density gradients at high inlet velocity cause difficulties. In order to correctly predict turbulent flames if blend fuels, it is necessary to validate the model's capability for hydrogen flames and hydrocarbon flames separately. In this study, pure hydrogen-air turbulent nonpremixed flames are numerically investigated. The configuration used is a co-flowing axisymetric turbulent non-premixed hydrogen flame, which is experimentally investigated by Barlow and Carter (1994) and Flury and Schlatter (1997). The model uses two turbulence closures that are the k-epsilon model and the Reynolds Stress Model (RSM) coupled with the steady strained laminar flamelet model. The performance of the k-epsilon and the RSM models are particularly discussed in the locations close to the nozzle exit. The results obtained demonstrate that the strained steady laminar flamelet approach based on the k-epsilon and the Reynolds stress turbulence models is, in general, capable of predicting this hydrogen-air flame at atmospheric pressure. Comparisons with measurements indicate that the predictions are sensitive to turbulence modelling and differential diffusion in the near-field region whereas the far-field region is influenced only by turbulence modelling. The RSM model gives better results than the k-epsilon model predictions close to the nozzle exit due to its corresponding turbulence parameters that are modelled more accurately. However, because of unity Lewis number assumption in the flamelet library generation, air entrainment is found to be not well predicted by the two turbulence models. Downstream, the k-epsilon model performs better and the predictions are very close to experimental data.