Speckle projection profilometry (SPP) encodes depth information of a scene by projecting a single random speckle pattern and establishes the global correspondences between stereo images using speckle matching technology, thereby achieving a single-shot three-dimensional (3D) reconstruction. However, it is still difficult to encode a globally unique feature for every pixel in an entire measurement space by projecting only a speckle pattern due to the measured object surface with complex reflection characteristics and the perspective differences between stereo cameras. The resulting mismatching problem leads to the low measurement accuracy of SPP, making it difficult to meet the high-precision measurement requirements of some industrial scenarios. In this study, we propose a speckle structured-light-based 3D imaging technique and its sensor design method using a vertical-cavity surface-emitting laser (VCSEL) projection array. The proposed 3D structured-light sensor integrates three miniaturized speckle projection modules to project a set of speckle patterns with different spatial positions, spatially and temporally encoding the depth information of the measured scene efficiently. In addition, a coarse-to-fine spatial-temporal speckle correlation algorithm is proposed to improve the measurement accuracy and reconstruct the fine shapes of complex objects. Experiments, including precision analysis, 3D model scanning, detection of small target metal parts, and measurement of complex scenes, indicate that the proposed 3D structured-light sensor can realize high-precision 3D measurements at a long distance over a large field of view, which can further be applied to industrial scenarios such as part sorting and robot stacking.