I have a green vein protruding from below my rright eye... as it is very close to my eye I can't undergo any laser treatment... is there any natural way of getting rid of it?please help!

Not sure what you mean by natural.. a vein can be removed by stripping (cutting two ends and pulling it out) if a laser can't be used. See a plastic surgeon.

If you mean a way to do it yourself? Not possible. There isn't any home remedy or special home made ointments to apply that will help.