This paper presents a new Bayesian sparse learning approach to select salient lexical features for sparse topic modeling. The Bayesian learning based on latent Dirichlet allocation (LDA) is performed by incorporating the spike-and-slab priors. According to this sparse LDA (sLDA), the spike distribution is used to select salient words while the slab distribution is applied to establish the latent topic model based on those selected relevant words. The variational inference procedure is developed to estimate prior parameters for sLDA. In the experiments on document modeling using LDA and sLDA, we find that the proposed sLDA does not only reduce the model perplexity but also reduce the memory and computation costs. Bayesian feature selection method does effectively identify relevant topic words for building sparse topic model.