For a stereo matching method based on deep learning, network architecture is critical to ensuring the algorithm's accuracy; efficiency is also an important factor to consider in practical applications. A stereo matching method with a sparse cost volume in the disparity dimension is proposed herein. The three-dimensional sparse cost volume is created by shifting right-view features with a large step to substantially reduce the memory and computational resources in a three-dimensional convolution module. The matching cost is nonlinearly sampled via multiclass output in the disparity dimension, and the model is trained by merging two types of loss functions, such that the proposed method's accuracy is improved without any notable reduction in efficiency. The proposed algorithm reduces running time by about 40% while improving accuracy compared with the benchmark algorithm on the KITTI test dataset.