This can be done with
 a small piece of code. Find and open the attributes.phtml file. This 
file can be found here:/app/design/frontend/[theme 
name]/[package name]/template/catalog/product/view/attribute.phtml
Open the file and search for the following lines:
<?php foreach ($_additional as $_data): ?>
    <tr>
        <th class="label"><?php echo $this->htmlEscape($this->__($_data['label'])) ?></th>
        <td class="data"><?php echo $_helper->productAttribute($_product, $_data['value'], $_data['code']) ?></td>
    </tr>
<?php endforeach; ?>
Replace the entire foreach loop with the following lines of code:
<?php foreach ($_additional as $_data): ?>
    <?php $_attribute = $_product->getResource()->getAttribute($_data['code']);
    if (!is_null($_product->getData($_attribute->getAttributeCode())) && ((string)$_attribute->getFrontend()->getValue($_product) != '')) { ?>
    <tr>
        <th class="label"><?php echo $this->htmlEscape($this->__($_data['label'])) ?></th>
        <td class="data"><?php echo $_helper->productAttribute($_product, $_data['value'], $_data['code']) ?></td>
    </tr>
    <?php } ?>
<?php endforeach; ?>
<?php foreach ($_additional as $_data): ?>
    <?php $_attribute = $_product->getResource()->getAttribute($_data['code']);
    if (!is_null($_product->getData($_attribute->getAttributeCode())) && ((string)$_attribute->getFrontend()->getValue($_product) != '')) { ?>
    <tr>
        <th class="label"><?php echo $this->htmlEscape($this->__($_data['label'])) ?></th>
        <td class="data"><?php echo $_helper->productAttribute($_product, $_data['value'], $_data['code']) ?></td>
    </tr>
    <?php } ?>
<?php endforeach; ?>