You need to make the call to setDate separately from the initialization call. So to create the datepicker and set the date in one go:

$("#mydate").datepicker().datepicker("setDate", new Date());

Why it is like this I do not know. If anyone did, that would be interesting information.

You have to initialize the datepicker before calling a datepicker method.

$("#mydate").datepicker().datepicker("setDate", new Date());
//-initialization--^          ^-- method invokation

<link href="https://code.jquery.com/ui/1.9.2/themes/base/jquery-ui.css" rel="stylesheet" />
<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script>
<script src="https://code.jquery.com/ui/1.9.2/jquery-ui.js"></script>
<input type="text" id="mydate" />

Here is a Working JSFiddle.

_{P.S: This assumes that you have the correct date set in your computer}

Its very simple you just add this script,

$("#mydate").datepicker({ dateFormat: "yy-mm-dd"}).datepicker("setDate", new Date());

Here, setDate set today date & dateFormat define which format you want set or show.

Hope its simple script work..