The direct-quadrature method of moment (DQMOM) and transported PDF (TPDF) approaches have been adopted to predict the precise structure of turbulent $CH_4$-air piloted jet flame. To realistically account for precise turbulent flame structure of turbulent jet flame, the mathematical formations of the transported PDF method are based on the joint-composition PDF model together with IEM mixing process. To minimize computational burden, the steady flamelet library is utilized to account for non-equilibrium chemistry. For unconditional means and conditional scatters for species mass fraction and temperature, comparison between predictions and measurement are made. Numerical results obtained by DQMOM and TPDF are reasonably well agreed with experimental data in terms of the mean and rms of species mass fraction and probability density function.