Direct numerical simulations for turbulent diffusion flames were conducted to clarify the relationship between the flow parameters and the fractal parameters such as fractal dimension and inner cutoff of the flame front. The fractal dimension increases with Reynolds number Re, and reaches the value of 1.44 at Rex = 252. The inner cutoff, calculated by the box counting method, is two to three times that of the enstrophy based microscale and is very close to the scale of maximum enstrophy dissipation. To construct the fractal dynamic subgrid-scale model the probability density function of the scalar gradient on the flame front was calculated. The behavior of the filtered PDF was also investigated. Filtered mean scalar gradient on the flame front shows a cutoff, which is about two times that of the inner cutoff of the flame front. The results we have obtained show that large eddy simulations for turbulent diffusion flames by using the fractal dynamic subgrid-scale model may be possible.