Spectral imaging in biological tissue is an important detecting method in the biomedical field. Affected by the scattering effect of biological tissue itself, the scattered light passing through such tissues forms a group of chaotic speckles in the detector, which can not be imaged directly. Many methods have been proposed to focus and image through or in the scattering media. However, at present, it is still a challenge to realize non-invasive, non-wavefront-shaping spectral reconstruction in scattering media. Spectral intensity transmission matrix technology was first used to realize spectral retrieval from the speckle pattern through scattering media. This method requires an optical fiber spectrometer to obtain spectral information from speckle signals, although the spectral measurement system composed of multimode fiber has a high spectral resolution, its anti disturbance performance is poor, the spectral intensity transmission matrix of the fiber requires pre-calibrated, and it requires high stability of the mechanical structure. Spectral imaging can also be realized by matrix decomposition which requires a scanner to scan the pixels of the imaging surface to obtain the spectral data cube, and then compress and reconstruct it. However, the structure of the experimental system is complex. Moreover, both of these two methods can not analyze the spectra of different chemical substances through scattering media. Recently, the matrix transmission technology combined with the algorithm of the nonnegative matrix decomposition method has been proved to realize the 2D focus and imaging of fluorescent targets through the scattering medium. Although it is still unable to distinguish or retrieve the spectra of different chemicals in the scattering medium, in the case of multiple input modes, the detector receives multiple information of the target, which just provides sufficient data support for spectral analysis.Therefore, inspired by these two methods, we proposed a novel Nonnegative Matrix Factorization-based method, combined with the multiple input modes as the illumination to realize multispectral reconstruction of targets in biological tissue in a non-invasive way. This technique can be implemented in two steps. Firstly, the information of the hidden target is obtained by the optical method, and secondly, the spectra can be reconstructed by the computational method. In the first step, we utilize a phase-only SLM to modulate the laser source and generate multiple random input modes to illuminate the hidden targets behind the scattering media. Then an imaging spectrometer is employed to capture the spectral and spatial information of the hidden targets through a non-invasive detection optical structure. In this step, each input mode generates a spatial-spectral 3D image in the imaging spectrometer that can be compressed as a piece of mixed spectral information which can be resolved in the computational step. After achieving a series of mixed spectral information, that can be reshaped and stored into a 2D matrix in the second step. And the spectra information of the hidden object can be retrieved using the Nonnegative Matrix Factorization algorithm from the 2D matrix.The feasibility of this algorithm is verified by simulation experiments. We first test the samples with two spectral components and calculate the root mean square error and correlation coefficient between the reconstructed spectra and ideal spectra. Then, we carry out similar simulation experiments on samples with more spectral components and analyze the factors affecting the quality of spectral reconstruction from two aspects: the number of input modes and the similarity between two original spectra. The simulation results indicate that this method can quickly distinguish the multiple targets in the scattering medium and reconstruct the spectrum of each chemical of the targets simultaneously. And the reconstructed spectra have a high spectral correlation (greater than 0.99) and low root mean square error (less than 0.02) which means a reliable reconstruction. It also shows that more input modes and lower similarity among each original spectrum can improve the quality of spectral reconstruction. Finally, an example is given to illustrate the application of the proposed technique in scattering imaging. More than that, the method escapes the physical access to the tissue and is not only suitable for any kind of linear excitation signal but also provides a new way to resolve multiple spectra from the aliasing information. Moreover, it provides technical support for the resolution, focusing, and signal enhancement of multiple targets in the scattering medium.