Klaus, who is played by Joseph Morgan, is expected to make his first appearance on the show in the April 21 episode.
Speaking to Entertainment Weekly, Graham said: "I think [the viewers will] be just as freaked out as we all get when we're in his scenes."
Graham also joked that she hopes fans don't confuse Morgan with his character.
"I hope that toward the end of the season, and into next season, that fans are really able to distinguish between the characters and the actors, because he's doing such a phenomenal job as Klaus," she said. "I want people to really see that and not be like, 'Oh I hate you, you're such an asshole trying to kill Elena!'
"He's just an actor... By the end of the season he might be either really hated or really loved."
The Vampire Diaries continues in the US on Thursdays at 8/7c on The CW and returns in the UK on Tuesday at 9pm on ITV2.
> Ooh, a peek at Klaus on 'Vampire Diaries'!