In this paper, the Eulerian Stochastic Field (ESF) model in the Transported Probability Density Function (TPDF) class model is combined with the Flamelet Generated Manifolds (FGM) model. This method solves the joint probability density function transport equation by ESF method that considers the interaction mechanism between flame and turbulence with high precision. At the same time, by making use of the advantage of the FGM model, this model is able to incorporate the detailed chemical reaction mechanism (GRI 3.0) with acceptable computational cost. The new model has been implemented in the open source CFD suite-OpenFOAM. Validation of the model has been carried out by simulating the Sandia flame series (three turbulent piloted methane jet flames) issued by the National Laboratory of the United States. The accuracy and advancement of the ESF/FGM turbulent combustion model are verified by comparing the LES results of the new model with the rich experimental data as well as the RANS results. The results demonstrate that the model has a strong ability in capturing combustion phenomena such as extinction and re-ignition in turbulent flame, which is essential in the accurate prediction of the combustion pro-cess in real combustion devices, for example, aircraft engines.