A method based on wavelet transform for identifying nonlinear structure system is presented. The method employs complex Morlet wavelet, and perform continuous wavelet transform on free respond signal of a nonlinear structure. According to maximum value of modulus of wavelet coefficient, the wavelet ridges and wavelet skeleton are extracted, which can be used to identified instantaneous frequency and amplitude of signal, then the skeleton curve of nonlinear structure is obtain. In additional, a method based on singular value decomposition (SVD) is proposed to proceed the obtained result for decrease the influence of noise. At last, the effectiveness and accuracy of the addressed method are validated via a numerical simulation of structure model with cubic nonlinear stiffness.