In this paper, a new model for closing the sub-grid reaction rate is proposed based on the series expansion of the chemical source term around the filtered value. For validation, large eddy simulations of a bluff-body stabilised premixed flame are performed at three different grid resolutions, and results are compared with experimental data. Simulations neglecting the sub-grid contributions of the source term are also conducted to examine the relative sub-grid contribution. The results show that the series model reproduces correctly key characteristics such as flame anchoring, recirculation zones and shear layers. Statistically, good agreement with experimental data is obtained by the series model, in terms of time-averaged profiles of velocity and its fluctuations, and temperature as well as the size of the recirculation region. With increasing mesh refinement, the “no-model” approach results improve and the predictions are similar (albeit always worse) to those of the series model.