Although convolutional neural network (CNN)-based stereo matching methods have become increasingly popular thanks to their robustness, they primarily have been focused on the matching cost computation. By leveraging CNNs, we present a novel method for matching cost aggregation to boost the stereo matching performance. Our insight is to learn the convolution kernel within CNN architecture for cost aggregation in a fully convolutional manner. Tailored to cost aggregation problem, our method differs from handcrafted methods in terms of its convolutional aggregation through optimally learned CNNs. First, the matching cost is aggregated with cost volume unary network, and then optimized with explicit disparity boundary, estimated through disparity boundary pairwise network, within a global energy minimization. Experiments demonstrate that our method outperforms conventional hand-crafted aggregation methods.