To protect the extreme-ultraviolet (EUV) mask from contaminations, the EUV pellicle is required. Internal temperature of EUV pellicle is increased during exposure process and then, thermal stress is also varied owing to increased temperature of EUV pellicle, so that the EUV pellicle will be broken. The cooling system by hydrogen gas (H<sub>2</sub>) flow is used to reduce internal temperature of EUV pellicle during exposure process. In order to determine the effect of cooling, we simulated variation of temperature and thermal stress for EUV pellicle membranes by using finite element method (FEM). Also, we considered a film coefficient with a few nanometer EUV pellicle thickness as simulation parameter. As a result, we determined that the cooling system of EUV pellicle by using H<sub>2</sub> flow is efficient to decrease temperature and thermal stress of EUV pellicle during exposure process.