A spectral camera based on the ghost imaging via sparsity constrains acquires a three-dimensional spatial-spectral data cube of information about a target in a single exposure. However, the spectral resolution and signal-to-noise ratio are limited, since the speckle field with different wavelengths are at the same location in the detector. To deal with these issues, a system which utilizes a flat-field grating to disperse the optical fields with different wavelengths in the detector to realize hyperspectral camera based on the ghost imaging via sparsity constraints is demonstrated. Through theoretical derivation of the imaging process, the correlation function of the system is obtained, and the derived result is verified by the experiments and numerical simulations. Under guaranteeing the advantages of previous ghost imaging spectral camera spectral camera, the proposed system can modulate the spatial and spectral resolution separately, meanwhile, the signal-to-noise ratio becomes controllable. Additionally, the measurement matrix will be better optimized according to the characteristics of optical fields with different wavelengths to improve the quality of imaging in the future.