In this paper, the additivity principle of scattering spectrum is proved with bidirectional reflectance distribution function theory coupled with the reference of Lambert-Beer law. For planar diffuse system with non-interacting between material particle, there is no interference, diffraction, fluorescence, spectral conversion, down conversion and other mutual conversion effects between the light source and incident surface material. Furthermore, in the context of non-photochemical phenomenon, nonlinear effects and in accordance with the law of conservation of energy, the material scattering spectrum irradiated by single or multiple light source equal to the linear superposition of the material scattering spectra of each material, which is called the additivity of scattering spectrum. In the experiment, the additivity principle is tested under different lighting conditions and material proportions. It is found that the maximum relative errors are 2.64% and 2.35% for the single and multiple light sources, respectively, which are less than those of theoretical results. Thus, it is shown that the scattering spectrum of material has the additive property which is independent from different lighting conditions and diverse materials and the different proportion of materials. This theory may give a useful method and theoretical reference for extracting feature and recognizing scattering spectra of complex systems. The first propose of the additivity of scattering spectrum provides not only the exact theoretical basis and effective analysis method for the extraction and recognition of complex structures characteristic scattering spectrum and has an important reference value for the experimental analysis and applied research.