Edit in JSFiddle

$(".btn").click(function(){
	var jsonDate = $(".inp").val();
	var date = new Date(parseInt(jsonDate.substr(7)));
    $(".date").text(date);
});

<form>
    <input type="text" class="inp" value='"/Date(1443657600000)/"' />
    <input type="button" value="Parse" class="btn" />
</form>
<div class="date"></div>