Yes it does have natural caffeine.
The average amount of caffeine in an 8-oz (230-ml) serving of green tea is around 35 mg. However, this can vary. The actual amount can be anywhere between 30 and 50 mg per 8-oz serving.
Since the caffeine in green tea occurs naturally, the amount depends largely on the variety of tea plant, its growing conditions and the way it is processed and brewed. For example, tea made with older leaves usually has less caffeine than tea made with younger tea leaves.
The amount of caffeine in your drink can also be influenced by the type of green tea you choose and how you prepare it. For example, bagged teas tend to be more caffeinated than loose leaf teas. This may be because the tea leaves in tea bags are crushed up, so more caffeine is extracted and infused into the drink.
Additionally, powdered green teas like matcha have a higher caffeine content than both bagged and loose green tea.