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Many vision applications have been formulated as Markov Random Field (MRF) problems. Although many of them are discrete labeling problems, continuous formulation often achieves great improvement on the qualities of the solutions in some applications such as stereo matching and optical flow. In continuous formulation, however, it is much more difficult to optimize the target functions. In this paper, we propose a new method called fusion move driven Markov Chain Monte Carlo method (MCMC-F) that combines the Markov Chain Monte Carlo method and the fusion move to solve continuous MRF problems effectively. This algorithm exploits powerful fusion move while it fully explore the whole solution space. We evaluate it using the stereo matching problem. We empirically demonstrate that the proposed algorithm is more stable and always finds lower energy states than the state-of-the art optimization techniques.