It's not about what we think but rather about what is in green tea *

But yes, green tea does contain caffeine and depending on how tolerant / how much you're used to it you'll either get a kick out of it or rather not. It's not as stimulating as a cup of coffee, for example but still does contain caffeine. Green tea is a healthy beverage in general, by the way.
* This isn't meant to sound mean or anything but for somebody who's been drinking lots of coffee for an extended period of time a cup of green tea won't do much. However, if you haven't been consuming caffeine rich consumables green tea will be a great start.