Comparing with nonlinear ultrasonic nondestructive testing method using harmonic signals and modulation methods, the local defect resonance（LDR） inter-modulation effect can greatly enhance the nonlinear behavior between the damaged interfaces,also,it uses the modulation between input signal and LDR frequency thus the input signal is simplified. When the excitation signal satisfies the specific frequency condition, the local resonance is produced at the micro-defect or damage area under ultrasonic excitation, which leads to the high order harmonics, subharmonics and the inter-modulation between input frequency and local damage resonance frequency in the response signal. In this paper, a single degree of freedom nonlinear model for damage local resonance effect was constructed, considering both quadratic and cubic stiffness nonlinearity, and analyzed using multi-scale method to explain the mechanism of local resonance modulation effect. Experiment of a carbon fiber composite plate with impact damage was carried out to verify the results of theoretical model analysis and the feasibility of the damage local resonance internal modulation method applying to nonlinear damage detection. Result shows that using LDR inter-modulation effect can effectively detect the impact damage of composite plate.