As one of the main experimental facilities in the Japan Proton Accelerator Research Complex (J-PARC), an intense spallation neutron source (JSNS) driven by a 1 MW proton beam is being constructed. Cryogenic hydrogen at supercritical pressure is selected as a moderator. The total nuclear heating at the moderators is estimated to be a 3.7 kW. A hydrogen system to cool the moderators has been designed. The most severe off-normal event for the cryogenic hydrogen system is considered to be a hydrogen leak when a pipe cracks. In such a case, the hydrogen must be discharged to atmosphere quickly and safely. An analytical code that simulates the pressure change during a hydrogen leak was developed. A pressure rise analysis for various sized cracks was performed, and the required sizes for relief devices were determined. A safety valve size is phi 42.7 mm and a rupture disc for vacuum layer should have a diameter of 37.1 mm, respectively.