The Scots are looking to make history and win their third consecutive match in the competition, having beaten Italy and Ireland in their last two matches.
The 27-year-old believes that Scotland's home form will come into play against the Welsh.
"Of course we're confident. We've got a good team, we're on our home ground and it's a sell-out. The fans were brilliant against Ireland," Grant told Scotsman.com.
"It's not often, when you're in the game and focused on your job, that you hear the crowd, but they were amazing against Ireland. They gave us the strength to grind out the win in the last 20 minutes.
"It's a good feeling when you're out there, you know you're on top and the crowd get behind you at the scrum. It gave us that extra buzz, the extra push needed. Given that we've won two and we're at home, sure, we can win this game."
Scotland host Wales at Murrayfield on Saturday.