소울해커님의 도움으로 이미지 저장은 잘되고 있습니다.
아래 같은 식으로 URL 이미지를 저장하고 있습니다.
<!--CodeS-->
procedure TForm_Pic.GetWebImage(AImageURL: String);
var
ImageStream: TMemoryStream;
URI: TidURI;
ImagePath: String;
JPI: TJPEGImage;
HTTP: TIdHTTP;
begin
  ImageStream := TMemoryStream.Create;
  HTTP := TIdHTTP.Create(Self);
try
  HTTP.Get(AImageURL, ImageStream);
  ImageStream.Position := 0;
  JPI := TJPEGImage.Create;
try
  JPI.LoadFromStream(ImageStream);
finally
  Image1.Picture.Assign(JPI);
  ImageURL := TrimRight(ImageURL);
  cutURL := RightStr(ImageURL,17);
  JPI.Free;
end;
finally
  ImageStream.SaveToFile('.\image\'+ cutURL);
  ImageStream.Free;
  HTTP.Free;
end;

end;

procedure TForm_Pic.Button1Click(Sender: TObject);
var
LineNo : Integer;
begin

   for LineNo := 0 to ListBox1.Items.Count -1 do
  begin
    ImageURL := ListBox1.Items[LineNo];
    GetWebImage('http://www.delphi.co.kr/' + ImageURL);
    Application.ProcessMessages;
  if LineNo = ListBox1.Items.Count -1 then begin
    Application.MessageBox('사진다운로드가완료