A latent Beta-Liouville allocation model is proposed.The proposed model is learned using a principled variational approach.The model is applied to the challenging problems of visual scene and text categorization, and action recognition. There has been a constant desire for proposing new machine learning approaches for count data modeling. One of the most referred approaches is the latent Dirichlet allocation (LDA) model (Blei et?al., 2003b). LDA has been shown to be a reliable model for count data classification. It is based, however, on the consideration of the Dirichlet distribution, as a prior, which modeling capabilities have been challenged recently and some alternative priors have been proposed. One of these priors is the Beta-Liouville (BL) distribution that we will consider in this work to provide an alternative to the LDA model. In order to maintain consistency with the original model we shall call our resulting model, latent Beta-Liouville allocation (LBLA). Like the LDA, the LBLA model uses a variational Bayes method for learning its hidden parameters. It will be shown that LDA is a special case of the LBLA model that we will show its merits, in comparison to the LDA model, via three distinct challenging applications namely text classification, natural scene categorization, and action recognition in videos. We will show that the LBLA model results in improved modeling accuracy in return for a slight increase in computational complexity. We conclude that our model can be considered as a more efficient replacement for the LDA model.