Aiming at the mathematical expressions of amplitude probability density functions of non-Gaussian vibrations, a Gaussian mixture model based probability density function (PDF) is proposed that is available for non-Gaussian vibra-tion signals. Firstly, the estimators of the higher-order moments of the non-Gaussian vibration process is obtained from the sample time history. Secondly, based on the quantitative relations of the even order moments of a given Gaussian process, along with the Gaussian mixture model, an equations set for evaluating the parameters in Gaussian mixture model is obtained. Lastly, based on the evaluated weighting factors and variances of the Gaussian elements, the mathe-matical model of non-Gaussian probability density function is obtained. Finally, the examples of simulated signals and measured signals have verified the validity of the presented method.