There is no precise record. But it was said that sunglasses were invented by Alessandro di Spina who was a italian monk lived in the middle ages, some one said that Roger Bacon, an english made it in the 13th centry, there are some statistics show that a chinese man made it , also in the 13the centry.
You can have a look at http://www.firmoo.com/answer/question/8040.html. Some people said that Chinese invented the first pair of sunglasses, some people hold the view that the first pair of sunglasses was sold by Sam Foster, and maybe he was the inventor. I don't know who invented them.
I have found this on wiki answer. Maybe it is more reliable. It is said that the Roman emperor used emeralds to avoid the sun getting in his eyes. And later Chinese people invented the sunglasses properly. You can have a look at http://wiki.answers.com/Q/Who_invented_sunglasses .