Make Sure you have copy the catalog/product/price.phtml in your current theme.

Then you have to add one line before <?php if (!$_product->isGrouped()): ?> line

<?php if ($_product->getPrice) > 0: ?>
    Whole file code
<?php endif; ?>

At last add <?php endif; ?>.

Make Sure you have copy the catalog/product/price.phtml in your current theme.

Then you have to add one line before <?php if (!$_product->isGrouped()): ?> line

<?php if ($_product->getPrice() > 0) : ?>
    Whole file code
<?php endif; ?>

At last add <?php endif; ?>.