Dense disparity map estimation from a high-resolution stereo image is a very difficult problem in terms of both matching accuracy and computation efficiency. Thus, an exhaustive disparity search at full resolution is required. In general, examining more pixels in the stereo view results in more ambiguous correspondences. When a high-resolution image is down-sampled, the high-frequency components of the fine-scaled image are at risk of disappearing in the coarse-resolution image. Furthermore, if erroneous disparity estimates caused by missing high-frequency components are propagated across scale space, ultimately, false disparity estimates are obtained. To solve these problems, we introduce an efficient hierarchical stereo matching method in two-scale space. This method applies disparity estimation to the reduced-resolution image, and the disparity result is then up-sampled to the original resolution. The disparity estimation values of the high-frequency (or edge component) regions of the full-resolution image are combined with the up-sampled disparity results. In this study, we extracted the high-frequency areas from the scale-space representation by using difference of Gaussian (DoG) or found edge components, using a Canny operator. Then, edge-aware disparity propagation was used to refine the disparity map. The experimental results show that the proposed algorithm outperforms previous methods.