Both are grammatically correct when spoken but they should be written: He is Swedish. He is a Swede. The second is especially important because a swede is also a kind of vegetable. That being said, I think there is a move away from describe nationality using nouns. So "He is Swedish" seems more natural to me.

Hey Marzi, they are both correct as the others have commented, but you just need to remember that both the name of the country and also the nationalities in English are capitalised :) For example: - He is from Australia - She is Australian

Both are correct, but you need to capitalize Swedish, and Swede (upper case "S")