Nonpremixed turbulent combustion is an important physical process in engineering.The interaction of turbulence and chemical reaction is the main problem in nonpremixedcombustion, in which turbulent mixing plays an important role. Turbulentconvection smears the fuel and oxidizer from large scales to small scales; through theconvection at these small scales and the di usion under the smallest turbulent scales,the mixing of fuel and oxidizer reaches molecular level; at last the chemical reactionoccurs. Therefore, mixing at small scales determines the chemistry reaction rate aswell as the heat release rate. In previous studies, the global statistical characteristics of turbulent mixing are adequately investigated. With the development of the LES in turbulent combustion, the characteristics of sub-grid scale (SGS) turbulent mixing need to be studied systematically. The multi scales and interactions among these scales of turbulent mixing process lead great challenges in the study of this problem. Direct numerical simulation (DNS) resolves all scales of a physical process. In the present work, DNSs of nonpremixed combustion in homogeneous and isotropic turbulence under various conditions are implemented. These data are first employed to study the SGS mixing characteristics systematically, then to test the proposed assumed double Gaussian FDF model of SGS scalar mixing. In present work, the new assumed FDF model is also tested in nonpremixed turbulent combustion in a priori way. These studies provide a fundamental understanding of the SGS mixing; the assumed double Gaussian FDF model proposed in the present work is proved to be an excellent alternative in large eddy simulation (LES) of turbulent combustion. The main innovative work of this thesis are as follows: 1. The nonequilibrium SGS mixing characteristics are investigated by first using DNS of developed homogeneous and isotropic turbulent mixing. This work confirms similar conclusions of SGS mixing in experimental studies of a turbulent jet. Using the conditional statistics of the filtered density function (FDF), conditionally filtered dissipation (CFD), conditionally filtered di usion (CFDIF),and so on, the SGS mixing characteristics are investigated. The results show that for large SGS scalar variance these quantities are bimodal, U shaped, transversally S shaped, respectively, which means the SGS mixing is non equilibrium. In the present work, the di usion layer like structure is investigated and visualized using DNS databases of steady turbulent scalar field in a cube, which confirms the inference that it leads locally non-equilibrium mixing characteristic. It is found from the present studies that, these non-equilibrium SGS mixing characteristics are consistent in both homogeneous and isotropic turbulence and a turbulent jet, which means they are general local mixing characteristics.These results on the SGS mixing characteristics provide a fundamental understanding for the SGS mixing and its modeling. 2. An assumed double Gaussian FDF model for the SGS mixing is proposed based on the SGS mixing characteristics. This work confirms that the passive scalar in a subgrid is separated into two relatively well mixed parts by a diffusion layer like structure. The fact is further stressed that the two well mixed parts are relatively independent and the scalar in each of them has an approximately Gaussian distribution. According to the SGS mixing characteristics an assumed double Gaussian FDF model for SGS mixing is proposed and its parameters are determined. The results predicted by the new model is supported by the DNS data of binary mixing in homogeneous isotropic turbulence and compared with the assumed Beta FDF model. The assumed double Gaussian is proved that it grasps the nonequilibrium SGS mixing characteristicsand has an excellent ability to prescribe the mixing in a subgrid. 3. In this work, the assumed double Gaussian FDF model is verified in a priori way in non-premixed turbulent combustion of one step, second order, isothermal reaction. Firstly, DNS databases of binary mixing in homogeneous and isotropic turbulence are used with equilibrium chemistry reaction to test the model. Secondly, flamelet model and flamelet progress method are used with the DNS databases of homogeneous and isotropic turbulent combustion to test the model. The results show that this model has a good predictive ability on SGS mixing. The model is an alternative for scalar mixing at subgrid scales in LES of turbulent combustion.