One simple way of doing it is setting the gridColor of JTable as transparent.
For Color use
and
set a (that is aplha) to zero. For transparency you can use any values to red, green, blue
JTable.setShowHorizontalLines(false) to only hide the horizontal lines.
JTable.setShowVerticalLines(false) to only hide the vertical lines.
JTable.setShowGrid(false) to hide both.