Even though multispectral imaging is considered very significant in biological imaging, it is only commonly used in microscopy in a 2D approach. Here, we present a Fluorescence Molecular Tomography system capable of recording simultaneously tomographic data at several spectral windows, enabling multispectral tomography. 3D reconstructed data from several spectral windows is used to construct a linear unmixing algorithm for multispectral deconvolution of overlapping fluorescence signals. The method is applied on tomographic 3D fluorescence concentration maps in tissue-mimicking phantoms, yielding absolute quantification of the concentration of each individual fluorophore. Results are compared to the case when unmixing is performed in the raw 2D data instead of the reconstructed 3D concentration map, showing greater accuracy when unmixing algorithms are applied in the reconstructed data. Both the reflection and transmission geometries are considered.