In this study, a method for producing green hydrogen from ammonia water using plasma cracking was proposed. Solid acid catalysts, FAU and MFI zeolites, were used as catalysts. Zeolites were prepared by varying the Si/Al molar ratio to investigate the relationship between the acid sites of the catalyst and the reaction activity. The plasma was directly discharged into the ammonia water to generate hydrogen from the decomposition of ammonia. The gaseous products from the ammonia decomposition by plasma were mostly hydrogen with some nitrogen. No CO2 was produced. Even when the catalyst was not injected, approximately 100 L/h of hydrogen was produced only by plasma discharge. The injection of the FAU or MFI zeolite catalysts improved the hydrogen production rate. The rate of hydrogen production obtained from the decomposition of ammonia water by catalyst and plasma irradiation was the highest for the FAU zeolite with the highest number of acid sites. The hydrogen production rate tended to increase in proportion to the number of acid sites in the catalyst.