Light passing through scattering medium will be scattered and result in a random speckle pattern on the focal plane of an imaging system. So we cannot directly observe the spatial and multi-spectral information of an object behind the scattering medium. Optical memory effect based speckle correlation imaging can realize the reconstruction of the object passing through the scattering medium. However, the previous research mainly focuses on the reconstruction of images at a single wavelength, and the spectral information of targets is easily dropped during the imaging process. In this paper, a multi-spectral scattering imaging method using snapshot micro-filter array multi-spectral detectors is proposed, and the imaging results of objects passing through the scattering medium under the wide-spectrum xenon light source illumination are obtained experimentally. A method of multi-spectral information reconstruction for objects passing through the scattering medium based on optical memory effect is proposed, and the detection imaging of multispectral information hidden behind the scattering medium is realized. Since the multi-spectral detectors provide low imaging quality, an image pre-processing method is proposed based on the autocorrelation to improve multispectral imaging quality of penetrating scattering media.