I am writing a game, that GUI has GridLayout structure. My problem is when my charachter moves from square to square it is jumping and I want to animate it. What do you think, is this possible?
Set your layout to null and use setLocation to move components. With null layout, in addition to adding a component to its container, you must also specify both a size and location for it to appear. You can use setBounds for this.
If you are serious in game programming. I recommend you to find a game library in Java and develop your game in lower levels. Check JMonkey Engine. They draw graphics with OpenGL and also have classes to integrate Swing/SWT components with your game...