There is diclosed a process for purifying hydrogen gas which comprises removing impurities such as nitrogen, oxygen, methane, carbon monoxide, carbon dioxide and moisture contained in a crude hydrogen gas by bringing the crude hydrogen gas into contact under heating with a hydride of a zirconium alloy such as Zr-V, Zr-V-Ni, Zr-V-Cr, Zr-V-Co, Zr-V-Fe, Zr-V-Cu, Zr-V-Ni-Cr, Zr-V-Ni-Co and Zr-V-Cr-Fe. By virtue of using the above Zr alloy hydride, the process enables highly advanced purification of crude hydrogen gas by removing such impurities as above to a level as low as 1 ppb or less in high safety and efficiency at low installation and running costs.