Single-shot three-dimensional (3D) shape measurement method based on digital speckle correlation (DSC) has high measurement precision and only requires one pair of speckle images. Nevertheless, the matching of speckles is time-consuming and may lead to some data defects at large gradient variations and edge regions. This paper proposes an end-to-end speckle matching network to achieve fast, precise, and edge-preserved 3D measurement. Compared with other networks, the proposed network reduces the redundant channels in the Siamese feature-extraction subnetwork and constructs cost volume by group-wise correlation, making it possible to provide efficient representations at low computational consumption, thus being suitable for high-precision 3D measurement in large resolution. A lightweight 3D stacked hourglass subnetwork is used to aggregate cost information and furthermore, an edge refinement module is integrated by leveraging the left speckle image as a guide to regular edge details. A reliable speckle binocular dataset is prepared with a specialized device in a simple procedure and the labels are produced from the DSC method. Experiments demonstrate that the proposed network can produce dense disparity maps with subpixel precision and reduce single-shot inference time to 0.13 s with less GPU occupation, which is a significant improvement compared with the traditional DSC method and other learning-based methods. Moreover, the experiment validates that measurement precision of the reconstructed plane can reach less than 0.03 mm, meeting the requirements of most industrial applications.