Generalized belief propagation is a popular algorithm to perform inference on large-scale Markov random fields (MRFs) networks. This paper proposes the method of accelerated generalized belief propagation with three strategies to reduce the computational effort. First, a min-sum messaging scheme and a caching technique are used to improve the accessibility. Second, a direction set method is used to reduce the complexity of computing clique messages from quartic to cubic. Finally, a coarse-to-fine hierarchical state-space reduction method is presented to decrease redundant states. The results show that a combination of these strategies can greatly accelerate the inference process in large-scale MRFs. For common stereo matching, it results in a speed-up of about 200 times.