After a hard searching this morning, I now get it work perfectly:
$(function() {
var API_KEY = 'xxxxxxxxxxxxxxxxxxxxxxxxxxxxx';
var PLAYLIST_ID = 'PLDvUaV28ulciewonYGknOdIw8lAJfXIzn';
var GOOGLE_API_URL = 'https://www.googleapis.com/youtube/v3/playlistItems?part=id%2C+snippet%2C+contentDetails&playlistId='+PLAYLIST_ID+ '&key=' + API_KEY + '&callback=showVideos';
$.ajax({
url: GOOGLE_API_URL,
dataType: 'jsonp',
crossDomain: true
});
window.showVideos = function(data) {
if (data.items && data.items.length > 0) {
$("#video").html('<iframe width="504" height="283" src="http://www.youtube.com/embed/'+data.items[0].contentDetails.videoId+'" frameborder="0" allowfullscreen></iframe>');
}
}
});