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Rayleigh and Hyper-Rayleigh scatterings (HRS) from the nano-particle SnO2 were measured. It is found that as the concentration of the colloidal SnO2 or radiation power increases, the first- and second-order polarizabilities decrease. The radiation power dependencies of the first- and second-order polarizabilities show two domains: in high radiation power domain, the first- and second-order polarizabilities are approximately constant, in low radiation power domain, the first- and second-order polarizabilities increase sharply and become sensitive to the radiation power. The behavior of the concentration dependencies of the first- and second-order polarizabilities of colloidal SnO2 particles is similar to that of the radiation power dependence. A detailed mechanism explaining these phenomena has been discussed.