The classic approach in developing Large Eddy simulation (LES) sub-grid-scale (SGS) combustion models is not satisfactory, the state-of-art models contain many tunable parameters which are dependent on different flow and combustion configurations. We propose a machine learning based approach to train a deep neural network (DNN) using high fidelity direct numerical simulation (DNS) combustion databases to learn LES combustion models. The learned model will be free from adjustable parameters and is expected to have superior performance at a low computational cost. Two neural network architectures, a simple DNN with stacked fully-connected layers and a convolution neural network (CNN), will be used to build the LES combustion models. A possible data augmentation strategy for embedding physical constraints will be explored. The performance of the learned models based on two different DNN architectures will be studied. The well learned DNN combustion model will also be used to suggest improvement for the existing algebraic models.The prediction of a learned LES model will be examined both in a prior test, using a new DNS database different from the ones the model is trained for, as well as in a posterior LES run employing the trained model.