int selectedIndex = yourJLIST.getSelectedIndex();
String [] ListData = new String[yourJLIST.getModel().getSize()];
for (int i = 0; i < ListData.length; i++) {
if(i == selectedIndex){
}else{
ListData[i] = yourJLIST.getModel().getElementAt(i);
}
}
yourJLIST.setListData(ListData);