When high performance is expected, vibrations are becoming a burning issue in adaptive optics systems. For mitigation of these vibrations, in this paper, we propose a method to identify the vibration model. The nonlinear least squares algorithm named the Levenberg-Marquardt method is adapted to acquire the model parameters. The experimental validation of the high performance of vibration mitigation associated with our identification method has been accomplished. Benefiting from this method, vibrations have been significantly suppressed using linear quadratic Gaussian control, where the root-mean-square of the residual vibrations has been reduced down to a portion of a microradian. Moreover, the experimental results show that with the model identified, vibrations ranging from wide low-frequency perturbation to high-frequency vibration peaks can be dramatically mitigated, which is superior to classical control strategies.