This paper proposes a stereo matching algorithm based on hierarchical belief propagation and occlusion handling. We define a new order for message passing in belief propagation instead of the scanline approach. The primary assumption is that a pixel with a well-defined minimum in its likelihood field is more likely to contain a correct disparity, when compared to a pixel having an ill-defined minimum with several local minima. The order for message passing is determined by the variance of likelihood field at each pixel. The variances evaluate the ambiguity of likelihood fields, and the messages are hierarchically updated along the gradient of ambiguity. The experimental results show that the proposed method estimates the disparities correctly in the hard regions such as large occlusions and textureless regions. The proposed algorithm is currently tied with the best performing algorithm on the Middlebury stereo site.