usrList : TStringList ;
.......
procedure TmainFrm.AddStr(usrStr:String);
var
index,cnt : Integer ;
begin
usrList := TStringList.Create ;
for cnt := 0 to yourListView.items.count-1
usrList.add(yourListView.items[cnt]);
usrList.Sort ;
// write back to yourListView from usrList...
end;
usrList.Free ;
end;