A moment method being able to handle detailed chemical kinetics has been developed in the context of presumed probability density functions (PDF). Temperature and composition are assumed to be independent statistically. Furthermore, both the PDFs are presumed as being the beta function distributions. The present method has been applied to a turbulent jet diffusion flame, which is opened as H3 flame on the international workshop on measurement and computation of turbulent non-premixed flames. It is found that the present method has a great potentiality, on the basis of the calculation result.