We present a local stereo matching method with a robust texture category-based matching cost and adaptive support window to deal with the disparity errors caused by repetitive patterns, occlusions, and nontextured cases. First, we decompose an input reference image into textured regions and nontextured regions. Then, different cost computation strategies are adopted for these two regions. For textured regions, we use the common absolute intensity difference and gradient similarity. For nontextured regions, we propose a matching cost computation method that is a combination of gradient and epipolar distance transform (EDT). In the cost aggregation step, we introduce an adaptive support window based on a modified linearly expanded cross skeleton. To obtain the cross skeleton, a depth edge detection technique and a triple expansion strategy are presented. The experimental results demonstrate that the proposed algorithm achieves outstanding matching performance compared with other existing local algorithms on the Middlebury stereo benchmark, especially in repetitive patterns, occlusions, and nontextured regions.