[ 다른 방법 1 ]
procedure TForm1.Button1Click(Sender: TObject);
var
  Flag: UINT;
  AppSysMenu: THandle;
begin
  AppSysMenu:=GetSystemMenu(Handle,False);
  Flag:=MF_GRAYED;
  EnableMenuItem(AppSysMenu,SC_CLOSE,MF_BYCOMMAND or Flag);
end;

[ 다른 방법 2 ]
procedure TForm1.FormCreate(Sender: TObject);
var
  hMenuHandle : HMENU;
begin
  hMenuHandle := GetSystemMenu(Form1.Handle, FALSE);
  if (hMenuHandle <> 0) then DeleteMenu(hMenuHandle, SC_CLOSE, MF_BYCOMMAND);
end;