Sometimes it is the way you make the tea. Green tea should not be made with boiling water - it scalds the tea and burns the essenses that emerge. Instead bring the water to just boiling. Let it cool a minute or two before pouring it over the green tea leaves.
then steep for up to 5 minutes. For many people, including myself, it is better to steep tea fewer minutes - say 1 to 3 instead of five. the weaker brew seems just as healthy, but easier on my stomach.
Also, what you have recently eaten before indulging in green tea may be reacting to the tea. Keep a journal of what and when you eat foods. this will help you be aware of what things make your stomach upset. It may not even be the tea.