Speckle structured light has become a research hotspot in recent years owing to its ability to obtain three-dimensional (3D) information by projecting only one image. However, when using speckle structured light to obtain 3D information, problems such as low number of matching speckle feature points and high mismatching rate are encountered. Therefore, the speckle feature-point extraction and matching algorithm is herein studied. Based on the analysis of the gray-distribution rule of speckle region, a method for extracting speckle feature points based on gray-value comparison is proposed. By comparing the gray value of relevant pixels on the window, coarse extraction is performed, and the response function of the feature point is defined to eliminate redundant detection. In terms of matching, speckle feature-point descriptors are established, and a multi-constrained propagation matching method based on descriptor information is proposed. First, the seed points with high matching degree were obtained through multi-constrained conditions, and the seed points were generated into a queue. Next, the unmatched speckle feature points in the descriptor were propagation matched using the descriptor information of the seed points. Experimental results show that the proposed algorithm increases the number of matches by more than 35% and reduces the mismatching rate to 0.12% compared to other algorithms.