The Baggies skipper believes that it will be a difficult game against Michael Laudrup's men, with whom they sit level on points in the Premier League.
"I think Swansea are a good side," Brunt told the club's official website. "We haven't done very well against them in recent seasons either.
"It's going to be a tough game but one we'd obviously like to build on after the good result we had against Sunderland at The Hawthorns.
"We owe Swansea one as well from the last three results against them. They're a good side and we saw down there this season they blew us away inside about 20 minutes. It's going to be a difficult game."
Steve Clarke's side lost 3-1 at the Liberty Stadium in November.