Chelsea face Middlesbrough at home on Sunday hoping to cement their position behind leaders Manchester United at the top of the table - but Grant is not expecting an easy ride with just seven games remaining.
Grant is remaining cautious as Chelsea prepare for the title run-in.
"We might drop points on the way," said Grant. "We need to go game by game.
"You need to keep your players focused all the time, especially now when you're coming up to the last games. We've done a good job up to now.
"We were many points behind Arsenal and now we're above them. But they're still in the race. That's my opinion. Not even one team will take all the points."