The latent Dirichlet allocation (LDA) model is a widely-used latent variable model in machine learning for text analyses. Inference for this model typically involves a single-site collapsed Gibbs sampling step for latent variables associated with observations. The efficiency of the sampling is critical to the success of the model in practical large scale applications. In this article, we introduce a blocking scheme to the collapsed Gibbs sampler for the LDA model which can, with a theoretical guarantee, improve chain mixing efficiency. We develop an O(log K)-step nested simulation, to directly sample the latent variables within each block. We demonstrate that the blocking scheme achieves substantial improvements in chain mixing compared to the state of the art single-site collapsed Gibbs sampler. We also show that when the number of topics is large, the blocking scheme can achieve a significant reduction in computation time compared to the single-site sampler.