The measuring technique combining a phase-shifting algorithm and Gray-code light has been widely used in three-dimensional (3D) shape measurement for static scenes because of its high robustness and anti-noise ability. However, in the high-speed measurement, phase unwrapping errors occur easily on the boundaries of adjacent Gray-code words because of the defocus of the projector, the motion of the objects and the non-uniform reflectivity of the surface. To overcome this challenge, a high-speed 3D shape measurement method based on shifting Gray-code light has been proposed in this paper. Firstly, the average intensity of three captured phase-shifting fringe images are used as a pixel-wise threshold to binarize the Gray codes and to eliminate most phase unwrapping errors caused by the non-uniform reflectivity, ambient light variations, and the defocus of projector. Then, the shifting Gray-code (SGC) coding strategy is proposed to avoid the remaining errors of phase unwrapping on the edge of the code words. In this strategy, no additional patterns are projected, and two sets of decoding words with staggered boundaries are built in the temporal sequences for one wrapped phase. Finally, the simple, efficient, and robust phase unwrapping can be achieved in the high-speed dynamic measurement. This proposed method has been applied to reconstruct 3D shape of randomly collapsing objects in a large depth range, and the experimental results demonstrate that it can reliably obtain high-quality shape and texture information at 310 frames per second.