The conditional moment closure(CMC) model has been implemented in context with the unstructured-grid finite-volume method which efficiently handle the physically and geometrically complex turbulent reacting flows. The validation cases include a turbulent nonpremixed CO/$H_2$/$N_2$ Jet flame and a turbulent nonpremixed $H_2$/CO flame stabilized on an axisymmetric bluff-body burner. In terms of mean flame field, minor species and NO formation, numerical results has the overall agreement with expermental data. The detailed discussion has been made for the turbulence-chemistry interaction and NOx formation characteristics as well as the comparative performance for CMC and flamelet model.