A multi-spectral ghost imaging scheme was proposed to address the issues of image blurring and degraded signal-to-noise ratio occurring under the push-broom mode by superposing the detected signals. Taking the multi-spectral camera based on ghost imaging via sparsity constraints as the imaging system, in this scheme, adjacent frames of detected signals are shifted superposed, then the corresponding equivalent detection matrix is derived combining with the calibrated measurement matrix, and the image is reconstructed via compressed sensing algorithms. Simulation and experimental results show that:properly increasing the exposure time helps to improve the reconstruction quality; under the same exposure time, images reconstructed from the shift-superposed signals obviously have enhanced SNR than those from the original signals acquired via a single frame.