The work aims to study the random influence of uneven road surface and irregular vibration on the hydrogen supply system (package of the power supply system) when the hydrogen vehicle is driving, in order to ensure the safe use of hydrogen vehicle. Based on Ansys Workbench (finite element analysis software), the random vibration analysis of the hydrogen supply system was carried out by using the modal superposition method and inputting the power spectral density excitation in GB/T 4857.23—2012. The stress and displacement distributions of 1σ, 2σ and 3σ were obtained, the maximum stress occurred in the system saddle, while the maximum displacement occurred in the system frame. It is proven that the hydrogen system can be used safely and provides a basis and guarantee for the future research and PSD random vibration of more transportation packaging systems.