TSearchRec sr;
AnsiString Path;
int iAttributes = 0x000010;

if (FindFirst(Path, iAttributes, sr) == 0)
{
    do{
        if ((sr.Attr & iAttributes) == 0x000010)
        {
            if(sr.Name[1] != '.')
                DirectoryListBox1->Items->Add(sr.Name);
    }
    }while(FindNext(sr) == 0);
    FindClose(sr);
}

이렇게 수정을 해보시죠.