I used A* algorithm in my game to do path finding, since my character taked 1x1 grid, it worked well . But now my character takes grids 2x2 ... and I need a presicely character path finding, I can't simply change 2x2 grids to 1x1 grid... Is there any good algorithm can solve my problem? Any advice is welcomed....

If you character has size 2x2, he will use the same cells as the 1x1 character (using his top left corner, for instance) except that you will now have to take four cells into account to determine if a certain 1x1 cell is a valid position for the character's top left corner.

I'm sorry ,I am a fool...
Any 1x1 grids can change to 2x2 without any message miss....

You might want to take a look at the other thread I started on Clearance-based pathfinding. It sounds like HAA* might be a good fit for your problem.