Front end update_post_meta Help

your nonce action name is wrong use same as entered in wp_nonce_field('update_grn_data','grn_data'); and also you forget to echo nonce, try this

if ( isset( $_POST['grn_data'] ) &&  wp_verify_nonce($_POST['grn_data'],'update_grn_data') ) {
    //if nonce check succeeds.
    $postid = $_POST['post_id'];
    $data = $_POST['grn'];
    update_post_meta($postid,'grn',$data);
}

form

<?php
/* This file is to provide input fields to record data from Front End */
function grn_data($post_id) { ?>
    <div class="grndata">
        <label for="grn" id="grnhead">GRN</label>
        <div class="toggle-fedata">
           <?php
           $curgrn = 'grn';
           $grnval = get_post_meta($post_id, $curgrn, true); ?>
           <form method="post" action="">
              <?php echo wp_nonce_field('update_grn_data','grn_data'); ?>
              <input type="text" size="30" maxlength="30" name="<?php echo $curgrn; ?>" value="<?php echo $grnval; ?>" />
              <input type="submit" value="Save" />
              <?php var_dump($grnval); ?>
              <?php var_dump($curgrn); ?>
          </form>
      </div>
   </div>
<?php } ?>

now call the form

echo grn_data($post->ID);