uses
  Winsock;

{...}

function getIPs: Tstrings;
type
  TaPInAddr = array[0..10] of PInAddr;
  PaPInAddr = ^TaPInAddr;
var
  phe: PHostEnt;
  pptr: PaPInAddr;
  Buffer: array[0..63] of Char;
  I: Integer;
  GInitData: TWSAData;
begin
  WSAStartup($101, GInitData);
  Result := TstringList.Create;
  Result.Clear;
  GetHostName(Buffer, SizeOf(Buffer));
  phe := GetHostByName(buffer);
  if phe = nil then Exit;
  pPtr := PaPInAddr(phe^.h_addr_list);
  I    := 0;
  while pPtr^[I] <> nil do
  begin
    Result.Add(inet_ntoa(pptr^[I]^));
    Inc(I);
  end;
  WSACleanup;
end;


procedure TForm1.Button1Click(Sender: TObject);
begin
  Memo1.Lines := GetIps;
end;