procedure TForm1.Button1Click(Sender: TObject);
var
    i:integer;
begin
    for i:=ListView1.Items.Count-1 downto 0 do
    begin
       if ListView1.Items.Item[i].Selected =True then
        ListView1.Items.Delete(i);
    end;
end;

var
    i: integer;
begin
    for i := 0 to ListView1.SelCount-1 do
        ListView1.Selected.Delete;
end;

while Assigned(ListView1.Selected) do
    ListView1.Selected.Delete;