Gaussian signal is produced by ordinary random vibration controllers to test the products in the laboratory, while the field data usually is non-Gaussian. To synthesize non-Gaussian random vibration, both the probability density function (PDF) and the damage effects must be considered. A new method is presented in this paper to synthesize non-Gaussian random vibration that is characterized by running RMS (root mean square). The essential idea is to model the non-Gaussian signal by a Gaussian signal multiplied by an amplitude modulation function (AMF). A two-parameter Weibull distribution is used to model the PDF of the running RMS and to create the AMF. The shock response spectrum (SRS) is used to detect significant shocks within the non-Gaussian signal. A case study is presented to show that the synthesized non-Gaussian signal has the same power spectral density (PSD), kurtosis, PDF and fatigue damage spectrum (FDS) as the field data.