Multi-line structured light three-dimensional (3D) scanning measurement system enables to obtain the richer 3D profile data of the object simultaneously during one frame, ensuring high accuracy while structured light is deformed for the modulation by the object. Nevertheless, current calibration methods cannot fully take advantage of its high precision. In this paper, a fast and high-accuracy 3D measurement system based on multi-line lasers with a spatially precise structure via integrating a diffraction grating was proposed. This helps achieve precise calibration results of the light planes by introducing spatial constraint relations of the diffractive light, thus improving measurement accuracy. The operating principle and the workflow of the proposed system were described in detail. The measurement accuracy of the developed prototype was verified through contrastive experiments. At a working distance of 400 mm, the results show that the root mean square error (RMSE) of the proposed system is 0.083 mm, which is improved by 37.6% compared to the traditional calibration method of light planes for the ranging system. The system utilizing a grating that facilitates the integration of the device has great application value.