What brand of "green tea" are you drinking? What grade of "green tea" are you drinking? Do they come in a paper tea bag? Loose leaf? Green tea has such a large range. At the bottom end, you have generic tea bags that are simply labeled "green tea", these I find to be extremely harsh and taste like well, tea bags and maybe even "grass". Not to mention, if you're drinking green tea for health reasons, these green teas probably aren't really given you as much as you could be getting...
I drink a fair amount of tea (as well as coffee), and currently in my cupboard I have teas where they are naturally overwhelmingly sweet (nothing added), to a stronger "tea" flavour, to many others. The place I would start isn't with additives, or brewing methods, but I'd go to a proper "tea" shop, and get a good loose leaf tea. I don't know if your area has a good chinatown, but there's bound to be a good tea shop there somewhere. Otherwise, even a more European influenced tea shop, should have a wide variety of green teas. Regardless of the tea shop, make sure they let you smell (waft with your hands or the lid of the canister, some shops get grumpy if you stick your nose in) the tea. Does it smell grassy? Does it smell pleasant?
If your tea tastes grassy, the solution isn't to mask it. It's to find tea that doesn't taste like grass.
Edit: I should also add that to be careful of how you steep green tea. It's much more prone to oversteeping than a dark tea. It should be steep for less time and at a lower temperature. No hotter than around 90C for 2-4 minutes I'd say.