Cost aggregation is crucial to the accuracy of stereo matching. A reasonable cost aggregation algorithm should aggregate costs within homogeneous regions where pixels have the same or similar disparities. Otherwise, the estimated disparity map is prone to the wellknown edge-fattening issue and the problem of losing fine structures. However, current state-of-the-art convolutional neural networks (CNNs) mainly do cost aggregation with square-kernel convolutional layers that learn to adjust their kernel elements to make the actual receptive fields of the aggregated costs adapt to homogeneous regions with various shapes. This is a mechanism that easily leads to the above issues due to the translation equivalence and content-insensitivity properties of CNNs. To tackle these problems, a novel densely connected asymmetric convolution block (Dense-ACB) based on asymmetric convolutions is proposed to explicitly construct receptive fields with various shapes, which effectively alleviates the issues caused by mismatching shapes of receptive fields and homogeneous regions. The proposed Dense-ACB brings new insight to CNN-based stereo matching networks. Based on the proposed cost aggregation method, an efficient and effective stereo matching network is built, which not only achieves competitive overall accuracy compared with state-of-the-art models but also effectively alleviates the edge-fattening problem and preserves fine structures.