frame = new JFrame("Test");  
Toolkit tk = Toolkit.getDefaultToolkit();  
int xSize = ((int) tk.getScreenSize().getWidth());  
int ySize = ((int) tk.getScreenSize().getHeight());  
frame.setSize(xSize,ySize);  
frame.show();  
oppure 
    MyFrame myFrame = new MyFrame();
    myFrame.setVisible(true);
    myFrame.setExtendedState(myFrame.getExtendedState() | JFrame.MAXIMIZED_BOTH);