new added element in the top of JList is automatically selected

I am creating a JList using swing, I can display and select multiple items, also I can add a new element to it. However, when I select the first element of the list and add a new one to the top, I got two selected elements (the old one and the new one), but when I change the selection mode to single selection it works fine, is it possible to prevent this automatic selection and just keep the old one selected using multiple interval selection mode?
I used this link that contain an example using DataEventListner but I did not succeed to find a solution. Any help please?
Here is my list:

 public static void main(String args[]) {
    String labels[] = { "A", "B", "C", "D", "E", "F", "G", "H" };
    JFrame frame = new JFrame("Selecting JList");
    frame.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
    final DefaultListModel model = new DefaultListModel();
    for (int i = 0, n = labels.length; i < n; i++) {
        model.addElement(labels[i]);
    }
    JList jlist = new JList(model);
    jlist.setSelectionMode(
            ListSelectionModel.MULTIPLE_INTERVAL_SELECTION);
    JScrollPane scrollPane1 = new JScrollPane(jlist);
    frame.add(scrollPane1, BorderLayout.CENTER);
    JButton jb = new JButton("add F");
    jb.addActionListener(new ActionListener() {
        public void actionPerformed(ActionEvent actionEvent) {
            model.add(0, "First");
        }
    });
    frame.add(jb,BorderLayout.SOUTH);
    frame.setSize(640, 300);
    frame.setVisible(true);
}

I see that you basically copied the code in the link in your question. That example only deals with adding a single element to the JList when clicking the JButton. It does not deal with the JList selection

I was able to reproduce the behavior described in your question. It may be a bug in the implementation of JList or ListSelectionModel. The way I fixed it is to add code to method actionPerformed() that handles any existing JList selections.

Here is my modified version of method actionPerformed(). Note that all the rest of the code is unchanged. First I save the indexes of all the selected rows. Then I clear the existing selections. Then I add the new element to the JList. Now I need to re-select the rows that were selected before I added the new element. But note that I need to increment each index by one, because there is a new element at index 0 (zero).

jb.addActionListener(new ActionListener() {
    public void actionPerformed(ActionEvent actionEvent) {
        int[] indices = jlist.getSelectedIndices();
        jlist.getSelectionModel().clearSelection();
        model.add(0, "First");
        for (int index : indices) {
            jlist.getSelectionModel().addSelectionInterval(index + 1, index + 1);
        }
    }
});

From the documentation of JList#setSelectionMode(int): <br/>

> ListSelectionModel.SINGLE_SELECTION - Only one list index can be
> selected at a time. In this mode, setSelectionInterval and
> addSelectionInterval are equivalent, both replacing the current
> selection with the index represented by the second argument (the
> "lead").

try jlist.setSelectionMode(ListSelectionModel.SINGLE_SELECTION);

You can add this in your jb.addActionListner():

int x = jlist.getSelectedIndex();
    jlist.clearSelection();
    jlist.setSelectedIndex(x);

This should work just the way you want it to!