Move in list control

It is not possible to do this without deleting. You have to create a copy of the row at the new loaction and delete the initial row.

Searching the web for "clistctrl move item up down" gives you examples:
Copying/Moving Rows in CListCtrl[^]
c++ - Move an item up or down in a list box - Stack Overflow[^]

[EDIT]
To move items one step it would be possible to exchange them:

• Get item at selected index and store data in variable
  
• Get item at new position (index +/- 1) and store data in variable
  
• Set item at selected position with data from new position
  
• Set item at new position with data from selected position
  
• Change selection to new position
  

Untested example:

// Single row must be selected
if (1 != GetSelectedCount())
    return;
int sel = GetNextItem(-1, LVNI_SELECTED); 
// Move up or down
int next = bUp ? sel - 1 : sel + 1;
if (next < 0 || next >= GetItemCount())
    return;
CString strSel, strNext;
for (int i = 0; i < GetHeaderCtrl()->GetItemCount(); i++)
{
    strSel = GetItemText(sel, i);
    strNext = GetItemText(next, i);
    SetItemText(sel, i, strNext);
    SetItemText(next, i, strSel);
}
// Move selection
SetItemState(sel, ~LVNI_SELECTED, LVIS_SELECTED);
SetItemState(next, LVNI_SELECTED, LVIS_SELECTED);
SetSelectionMark(next);

[/EDIT]