I am considering your GridView Id as GridView1 and Delete button Id as lnkDelete.
1. To your LinkButton add style = "display:none"
2. Then place the following JavaScript code
 <script type="text/javascript" src="http://ajax.googleapis.com/ajax/libs/jquery/1.8.3/jquery.min.js"></script>
    <script type="text/javascript">
        $(function () {
            $("[id*=GridView1] td").bind("mouseover", function () {
                $(this).closest("tr").find("[id*=lnkDelete]").show();
            });
            $("[id*=GridView1] td").bind("mouseout", function () {
                $(this).closest("tr").find("[id*=lnkDelete]").hide();
            });
        });
    </script>