A method of third-order cumulants (TOC) based on singular value decomposition (SVD) is presented to effectively consider the nonlinear characteristic caused by micro-cracks in damage identification of reinforced concrete structures. Firstly, The singular values of the TOC of vibration acceleration signals are calculated, then the singular values of TOC are applied to describe and assess the severity of structure damage and structure state. The efficiency of the method is verified by an experimental test of two reinforced concrete simply supported beams which are gradually damaged. The results clearly show that the change trend of singular values of TOC are identical to the cracks propagation of experiment records, the singular values of TOC can effectively indicate the damage degree of beams, the results are satisfying and indicate that the method is effective.