The aims of this work were to study the non-Gaussian properties of random vibration during the raiway transportation, and to analyze the response of packages excited by the non-Gaussian random vibration. A novel approach was proposed to synthesize railway non-Gaussian random vibration which incorporated discrete Fourier transform method with EARPG(1) model. The amplitude was obtained based on the PSD curves of collected data. The EARPG(1) model was used to generate spiky data, the phase was calculated and shifted. Based on the amplitude and phase, the non-Gaussian random vibration signal required was synthesized. The package was simplified to a SDOF system, and the acceleration response of the system under non-Gaussian vibration condition was analyzed. The kurtosis of railway random vibration was bigger than 3, and the skewness was 0. So the railway random vibration belonged to symmetrical super-Gaussian vibration. The model presented in this paper could simulate railway random vibration with accuracy, and both the kurtosis and skewness error were less than 3% . The simulation results indicated that the natural frequency, damping ratio and the excitation kurtosis affected the response kurtosis and RMS value. The response kurtosis and RMS value could be effectively decreased by the proper choice of natural frequency and damping ratio of package, and the reliability of package could be increased through proper packaging design.