This is very easy. Vimeo has API. This is the Vimeo Simple API docs.

You should make a Video Request

To get data about a specific video, use the following url:

http://vimeo.com/api/v2/video/video_id.output

video_id The ID of the video you want information for.

output Specify the output type. We currently offer JSON, PHP, and XML formats.

So fow example getting this URL http://vimeo.com/api/v2/video/6271487.xml. You will get xml output, with video information.

Parse this for every video to get the thumbnail

Here’s approximate code in PHP:

$imgid = 6271487;
$hash = unserialize(file_get_contents("http://vimeo.com/api/v2/video/$imgid.php"));
echo $hash[0]['thumbnail_medium'];

Also you can do this with javascript.

function vimeoLoadingThumb(id){
var url = "http://vimeo.com/api/v2/video/" + id + ".json?callback=showThumb";
var id_img = "#vimeo-" + id;
var script = document.createElement( 'script' );
script.type = 'text/javascript';
script.src = url;
$(id_img).before(script);
}
function showThumb(data){
var id_img = "#vimeo-" + data[0].id;
$(id_img).attr('src',data[0].thumbnail_medium);
}

Show image:

<img id="vimeo-{{ video.id_video }}" src="" alt="{{ video.title }}" />

<script type="text/javascript">

vimeoLoadingThumb({{ video.id_video }});

</script>