Probabilistic topic models such as Latent Dirichlet Allocation (LDA) discover latent topics from large corpora by exploiting words’ co-occurring relation. By observing the topical similarity between words, we find that some other relations, such as semantic or syntax relation between words, lead to strong dependence between their topics. In this paper, sentences are represented as dependency trees and a Global Topic Random Field (GTRF) is presented to model the non-linear dependencies between words. To infer our model, a new global factor is defined over all edges and the normalization factor of GRF is proven to be a constant. As a result, no independent assumption is needed when inferring our model. Based on it, we develop an efficient expectation-maximization (EM) procedure for parameter estimation. Experimental results on four data sets show that GTRF achieves much lower perplexity than LDA and linear dependency topic models and produces better topic coherence.