The eddy dissipation concept (EDC) for turbulent combustion modeling was originally proposed by Magnussen in the Reynolds averaged Navier-Stokes (RANS) context. This study has extended it to the large eddy simulation (LES) framework. Since the fine structures in EDC are still not resolved in LES, they are modeled with SGS turbulent kinetic energy and its dissipation rate instead of the mean quantities in RANS. A new expression is proposed for the reacting fraction of the fine structures to alleviate the limitations of the original formula. Three fire cases including a 7.1 cm methane fire, a 30 cm heptane fire and a 30.5 cm methanol fire are simulated to verify the improved EDC (M-EDC), which has been implemented in the FireFOAM solver. The predictions from the M-EDC are found to be in reasonably good agreement with the measurements, while the original EDC tends to under-predict temperature and velocity.