In stereo matching, homogeneous areas, depth continuity areas, and occluded areas need more attention. Many methods try to handle pixels in homogeneous areas by propagating supports. As a result, pixels in homogeneous areas get assigned disparities inferred from the disparities of neighboring pixels. However, at the same time, pixels in depth discontinuity areas get supports from different depths and/or from occluded pixels, and resultant disparity maps are easy to be blurred. To resolve this problem, we propose a non-linear diffusion-based support aggregation method. Supports are iteratively aggregated with the support-weights, while adjusting the support-weights according to disparities to prevent incorrect supports from different depths and/or occluded pixels. As a result, the proposed method yields good results not only in homogeneous areas but also in depth discontinuity areas as the iteration goes on without the critical degradation of performance.