Three-dimensional (3D) shape acquisition of objects from a single-shot image has been highly demanded by numerous applications in many fields, such as medical imaging, robotic navigation, virtual reality, and product in-line inspection. This paper presents a robust 3D shape reconstruction approach integrating a structured-light technique with a deep learning-based artificial neural network. The proposed approach employs a single-input dual-output network capable of transforming a single structured-light image into two intermediate outputs of multiple phase-shifted fringe patterns and a coarse phase map, through which the unwrapped true phase distributions containing the depth information of the imaging target can be accurately determined for subsequent 3D reconstruction process. A conventional fringe projection technique is employed to prepare the ground-truth training labels, and part of its classic algorithm is adopted to preserve the accuracy of the 3D reconstruction. Numerous experiments have been conducted to assess the proposed technique, and its robustness makes it a promising and much-needed tool for scientific research and engineering applications.