i found this code wordpress.org . This code would work in author template.
<?php
global $wp_query;
$curauth = $wp_query->get_queried_object();
$post_count = $wpdb->get_var("SELECT COUNT(*) FROM $wpdb->posts WHERE post_author="" . $curauth->ID . "" AND post_type="post" AND post_status="publish"");
?>
<h2>Post Count: <?php echo $post_count; ?></h2>
But if you wish to use it somewhere else then replace $curauth->ID
with author id and post
with the post type you want
it should work .
All the best