function find_select(name)
{
 var select = document.getElementsByName(name);
 var find_str = document.getElementById('to_find_str').value;
 if(select)
 {
  select = select[0];
  var child = select.childNodes;
  var can=false,text='',len=child.length,is_end=true;
  for(var i=0;i<len;i++)
  {
   if(can)
   {
    text = child[i].text;
    if( text &&
     text.indexOf(find_str)!=-1)
    {
     //console.log(text);
     child[i].selected = true;
     var v = child[i].value;
     select.value = v;
     select.onchange(v);
     is_end = false;
     break;
    }
   }
   if(child[i].selected)
    can = true;
  }
  if(is_end)
   alert('已沒有匹配內容');
 }
}

<tr>
          <td><?php echo $L_SpecialActivityIdentifier?></td>
          <td>
    <select name="Activity[Identifier]" id="Identifier" onchange="change_activity(this.value)">
   <option value="">請選擇</option>
   <?php
   foreach ($ActivityTypes as $Row ) {
    echo '<option value="'.$Row['Identifier'].'" '.($Row['Identifier']==$Activity['Identifier']?'selected':'').'>'.$Row['Name'].'</option>';
   }
   ?>
    </select>
     -- <input value='' id='to_find_str' size=16 style="text-align:center;" /><input value='find' onclick='find_select("Activity[Identifier]")' type=button />
          </td>
      </tr>