This paper proposes a four-dimensional (4D) line-scan hyperspectral imaging system to acquire 3D spatial data and hyperspectral images covering from visible to short-wave infrared (Vis-SWIR) wavelength range. The system captures visible and near-infrared (VNIR) and SWIR hyperspectral images using two line-scan sensors, while 3D spatial data is acquired via a fringe projection profilometry subsystem. To align the VNIR and SWIR hyperspectral images, we utilize a line-scan homography method and propose a transformation method to register 3D spatial data with hyperspectral images. The mean reprojection error for hyperspectral image registration is 0.5396 pixels, and the registration of 3D spatial data with hyperspectral images achieves subpixel accuracy. Spatial accuracy is demonstrated with a root mean squared error (RMSE) of 0.1321 mm and a mean absolute error (MAE) of 0.1066 mm by measuring a standard sphere with a 20.0512 mm radius. The spectral resolutions are 11.2 nm in the VNIR range and 5 nm in the SWIR range. Two case studies were conducted: one involving a colorful object with rich features and colors, and another involving a potato before and after sprouting. Results from the measurement of a colorful object demonstrate the proposed system’s registration accuracy and image intensity variation across wavelengths, while the potato study highlights the system’s potential applications in the food industry.