@Ajax.ActionLink("titie", "List", new { id = Model.id },
   new AjaxOptions { UpdateTargetId = "someDiv", HttpMethod = "GET", OnComplete = "change(this)")},null)

  <script type="text/javascript">
   function change(link) {
    $(link).hide();
   }
  </script>

Ajax.ActionLink( string linkText,
             string action,
             object routeValues,
             AjaxOptions ajaxOptions,
             object htmlAttributes )

@Ajax.ActionLink("titie", "List", new { id = Model.id },
new AjaxOptions { UpdateTargetId = "someDiv", HttpMethod = "GET",
OnComplete = "change(this)")}, new {id = "linkToBeHidden"}})

<script type="text/javascript">

     $( "#linkToBeHidden" ).on( "click", function() {
               $('#linkToBeHidden').hide();
     });

</script>

@Ajax.ActionLink("titie", "List", new { id = Model.id },
  new AjaxOptions { UpdateTargetId = "someDiv", HttpMethod = "GET", OnComplete = "change")},
new { id="link" })

function change(){
    $('#link').hide();
}

@Ajax.ActionLink("titie", "List", new { id = Model.id },
new AjaxOptions { UpdateTargetId = "elementID", HttpMethod = "GET",
OnComplete = "HideMe()")}, new {id = "dummyId"}})

function HideMe()
{
$('#dummyId').hide();
}